He presented the science series "Eye on Research" from 1959 to 1963, and was the first (and initially sole) host of the long-running popular science show "Tomorrow's World" for 12 years from July 1965, reaching an audience of up to 10 million viewers. He was the presenter of the first live transatlantic broadcast from the US via Telstar in 1962, the first live telecast from Australia in November 1966, and interviewed South African surgeon Christiaan Barnard by telephone in 1967, within hours of the completion of the world's first heart transplant operation. Baxter also undertook commercial commissions. He was the presenter for the launch of Gillette's G2 Razors held at the Heathrow Hotel, London, in 1973. He left the "Tomorrow's World" programme in 1977, after disagreements with its new editor, Michael Blakstad, who described Baxter as "the last of the dinosaurs", while Baxter reputedly said he could not work with someone who arrived at the BBC each day on a bicycle.