Anthony Leslie Bastable was born in Hexham, Northumberland in 1944. After moving to Wembley, Middlesex, he attended Wembley Manor School from 1952 to 1955 and University College School in Frognal, London before briefly working for local newspapers. Whilst working as a freelance reporter he also taught British history, part time, at Buckingham College, Harrow.

In the early 1960s, Bastable applied for a job as a television news reporter for Southern Television, but was turned down for being "too young". Instead he was given a job presenting a children's programme. Within 18 months he was working for ATV as a presenter of children's shows, sports magazines and schools' programmes. In 1968 he moved to Thames Television and begun presenting Magpie, a new children's programme, with Susan Stranks and Pete Brady. Magpie was seen as a "groovier" version of the BBC's Blue Peter In 1972, he moved to become Magpie's producer. During his career, Bastable produced and presented many one-off programmes, including historical documentaries and current affairs programmes, and presented and commented on many outside and sporting events. For nine years Bastable presented the consumer protection series Money-Go-Round, and also presented shows such as Drive-in, Mind Over Matter, a programme he devised with Kit Pedler that investigated the paranormal and Database. In addition, he was often a panellist on radio shows and he narrated the Channel 4 nature programme "Profiles Of Nature".

Bastable later moved into independent production, and he produced training and promotional films for companies such as the Ford Motor Company, the National Bus Company, the Royal Navy, the Department of Transport and the Institute of Advanced Motorists. Bastable was also the co-author of two children's books and wrote biographies of John Cabot and Ferdinand Magellan, both of which were published in 2003. Tony Bastable was a qualified cricket umpire and founded the Institute of Cricket Umpires and Scorers.

Bastable married three times - firstly in 1969 to June Buchan, from whom he was divorced in 1971. In 1974 he married Jackie Colkett. They had a daughter but divorced in 1992. He married his third and final wife, Anita Westwood, in 2001. Bastable suffered from emphysema and died in the East Surrey Hospital, Redhill, Surrey in 2007 frompneumonia.