Batey [née Lever], Mavis Lilian (1921–2013), code-breaker and garden historian, was born on 5 May 1921 at 20 Crebor Street, Dulwich, London, the only daughter and younger child of Frederick (formerly Fred, later Stanley Frederick) Lever (1887/8–1971) and his wife, Lily Elizabeth, née Day (1888–1966). Her older brother, Stanley, was born in 1916. Her father was a postal worker and her mother a seamstress, and she was brought up in Norbury and Croydon. She attended the Coloma Convent Girls' School, in Tavistock Road, Croydon, where she discovered a talent for modern languages. In 1938 she registered at University College, London, for a degree course studying German with French; her professor was Leonard Willoughby, who had worked as a code-breaker in the Admiralty's room 40 during the First World War. She joined in the student support for Republican Spain, and the protests at the German embassy which followed Kristallnacht in November 1938, and in the spring of 1939, after the annexation of Prague had made a German university placement unwise, she went to the University of Zürich. She returned to England as war threatened, and in November 1939, rather than follow University College's evacuation to Aberystwyth, she gave up her studies and applied to the Foreign Office for war work.

Given her language skills, in January 1940 Mavis Lever was sent to the Government Code and Cypher School at Broadway Buildings, St James's, where she was taught to break commercial codes, providing intelligence to the Ministry of Economic Warfare on firms in neutral countries supplying goods to Germany. After impressing her superiors by realizing that the puzzling place named St Goch in a Morse code transcript was actually Stgo Ch, meaning Santiago, Chile, she was sent in March to the new Government Code and Cypher School station at Bletchley Park in Buckinghamshire. There she joined the Enigma research team led by Dilly Knox, with whom she worked closely until his premature death in 1943.

Mavis Lever played a critical role in two of Bletchley's great achievements: first, the breaking of the Italian Enigma, which allowed the Royal Navy to ambush an Italian fleet in the decisive action of 28 March 1941, which became known as the Battle of Matapan; and second, the breaking of the Abwehr Enigma in December of the same year, which allowed access to the German high command's secret intelligence service and its network of spies. On the latter she had worked with her colleague Margaret Rock, and Knox gave enormous personal credit to both, saying, 'Give me a Lever and Rock and I can move the universe' (Dilly, 140).

At Bletchley, Mavis Lever met and fell in love with a fellow code-breaker, (John) Keith Batey (1919–2010), a mathematician and 'wranglercove' from Cambridge (Dilly, 102). They were married at Holy Trinity Church, Marylebone, near Regent's Park, on Guy Fawkes' day, 5 November 1942. Mavis Batey continued to work at Bletchley until the end of the war, after which she and Keith (who joined the Commonwealth Relations Office) embarked on family life. In 1947 they travelled with a five-month-old daughter to Canada, where Keith worked in the high commissioner's office in Ottawa until 1951, before returning to England when he became private secretary to the secretary of state for Commonwealth relations. Their second child, a son, had been born in Canada, and a second daughter was born in 1954.

In 1955 the Bateys settled in Farnham, Surrey, when Keith became secretary of the Royal Aircraft Establishment at Farnborough. There Mavis devoted herself to bringing up their children, but it was while living in Farnham that she first became interested in landscape history and the work of W. G. Hoskins. She was inspired by the idea of being able to read the English landscape for its human history, later referring to Hoskins as her guru. She particularly admired Hoskins's approach to what he called 'observables', and later commented of the Oxfordshire landscape that 'it was all of a piece—villages, Roman roads, vernacular architecture, ridge and furrow, scholar gypsies, William Morris, [and] Capability Brown' (Garden Conservation Newsletter, 1995, 9).

In 1964 Keith Batey was appointed secretary of the Oxford University Chest (in effect the university's chief financial officer), a post he held until moving to become treasurer of Christ Church in 1972, and in 1965 the family moved to Oxford, which led to a long and fruitful new phase in Mavis's life. Their first home was the Old Town House at Nuneham Courtenay, which was part of the university estate, and more significantly part of the historic designed landscape of Nuneham Park. She later said,

When I cut my way into [William] Mason's flower garden, almost losing a small daughter in the undergrowth, I had the feeling not so much that it was a garden that was derelict, as that somebody had once tried to say something there.

Garden Conservation Newsletter, 1995, 8

She began to explore the history of the place, and to bring her Bletchley skills for understanding a coded language to bear on the English landscape garden.

The first fruit of Mavis Batey's new career was an impeccably researched and influential article in Oxoniensia in 1968, pinpointing Nuneham as the inspiration of Oliver Goldsmith's The Deserted Village. She became active in conservation rather than just academic history, serving on the committees of both the Oxfordshire Council for the Protection of Rural England and the Oxford Civic Society, and her interest was always wider than just gardens: she later recalled campaigning in 1967 for the protection of the watercress beds in the village of Ewelme, which as late as 2001 received a Heritage Lottery Fund grant for their conservation. In Oxford she lectured at the university department for continuing education, where she became a part-time tutor in 1970, and ran courses for the Workers' Educational Association on Oxfordshire landscape history as well as on gardens.

The Nuneham research introduced Batey to the Garden History Society, formed in 1965, and she agreed to become honorary secretary in 1972. She led the Garden History Society to develop as a campaigning conservation body rather than just a learned society, and in the first few years of her involvement it fought threats to many parks and gardens: road schemes at Beckley Park in Oxfordshire, Petworth in Sussex, Levens in Cumbria, and Chillington in Staffordshire, a sewage works at Audley End in Essex, and development proposals at Summerhill in Bath and in the vista from Vanbrugh Castle at Greenwich. In 1977, as part of the campaign to rescue the neglected masterpiece Painshill in Surrey, she put the case for funding to the parliamentary inquiry into the National Land Fund, and Painshill became the first landscape garden to benefit from grant aid from the new National Heritage Memorial Fund when it was formed in 1980.

On the strategic front, one of Batey's early successes was working with the Civic Trust to introduce the idea of the 'setting of a listed building' into the 1974 Town and Country Amenities Act, and in the same act to secure an amendment to the 1953 Historic Buildings and Monuments Act to allow grants for historic gardens as well as historic buildings—the first recognition of the idea in legislation. Following a speech to the Schwetzingen conference organized as part of European architectural heritage year in 1975, she got a resolution that 'historic parks and gardens should be recognised as essential components of European culture' (Painshill Park, 17).

The Garden History Society had already begun compiling an inventory of parks and gardens and in 1975 Batey met the secretary of state for the environment, Anthony Crosland, and, citing the Schwetzingen resolution, persuaded him of the need for government recognition of their importance. In 1977 Jennifer Jenkins, a great ally and chair of the Historic Buildings Council, set up a gardens sub-committee, and over the next six years Batey led the voluntary effort by the Garden History Society and others to compile county lists. These formed the basis for the national Register of Parks and Gardens of Special Historic Interest enabled in the 1983 National Heritage Act. Soon after the Historic Buildings Council was reformed as English Heritage in 1984, an advisory gardens committee was established on which Batey served for ten years.

Batey stepped down as the Garden History Society's secretary in 1985 and became its president, a role she held until 2000. In 1985 she received the Royal Horticultural Society's Veitch memorial medal, followed two years later by an MBE for 'services to the preservation and conservation of historic gardens'. Keith Batey retired from Christ Church in 1985, and in 1987 they moved from Oxford to Aldwick, near Bognor, where they bought West House, a Regency cottage orné, a few yards from the coast. From there she continued to take a leading role in the society's affairs and in the conservation movement. For many years she also continued to organize conferences and summer schools with Oxford University's department for continuing education. She worked with Kim Wilkie on the pioneering Thames landscape strategy of 1994, and on Garden History Society campaigns over golf courses, enabling development, and the plight of Victorian public parks as well as high-profile cases such as Mount Edgcumbe in Plymouth. In 1995 she led the society's successful lobbying of government to become a statutory consultee on planning applications affecting registered parks and gardens, which embedded the Register firmly in the planning system. Unfailingly encouraging to enquirers and generous with her research, she maintained a voluminous correspondence with academics and scholars around the world.

After many years of silence required by the Official Secrets Act, interest in Bletchley Park grew rapidly after the site was acquired by the Bletchley Park Trust in 1999 and Mavis Batey became a reliable source of information for researchers and authors. In 2001 she advised the actress Kate Winslet on her role as a female code-breaker in the film Enigma, and her memories were frequently cited in the many books now published on Bletchley and its work. In 2004 she advised the trust on a new American garden trail at Bletchley, planted with emblems of the USA states to commemorate the work of the 300 American personnel who worked there.

As a scholar Batey's interests were bound up with conservation campaigns, either stemming from or leading to them. She was the author of many books and articles for Garden History, Country Life, and other journals. Although she wrote on John Evelyn in the seventeenth century and on Gertrude Jekyll and arts and crafts gardens in the early twentieth, her principal interests lay in the eighteenth and early nineteenth centuries, and in particular in the relationship between landscape and literature. She published articles on William Gilpin and the picturesque, Keats's House in Hampstead, Jane Austen, Pope and Walpole, Morris and Ruskin. She was a champion of Lewis Carroll, in whose life and work she became interested during Keith Batey's time at Christ Church, when she could explore the college gardens which inspired Wonderland. She often claimed that her most successful book was Alice's Adventures in Oxford (1980), which remained in print for many years as a staple of the city's gift shops. Her other books included Oxford Gardens: the University's Influence on Garden History (1982), The English Garden Tour (1990, with David Lambert), Arcadian Thames (1994, with Henrietta Buttery, David Lambert, and Kim Wilkie), Regency Gardens (1995), Jane Austen and the English Landscape (1996), and Alexander Pope: the Poet and the Landscape (1999). In 2009 she published Dilly: the Man who broke Enigmas, an affectionate tribute to her mentor at Bletchley. She spent her final years at Barlavington Manor care home in Petworth, Sussex, and died there on 12 November 2013; she was survived by her three children.