1959-64 was for a different constituency: he narrowly gained Nottingham West in one of the biggest upsets of the election (Labour did terribly in Nottingham that year, I think partly due to a nasty row between the city council and the local police chief) and then inevitably lost it in 1964. There is actually an MP who served in the 1960s who's still in the Commons, but he's had interrupted service: David Winnick was elected for Croydon South (which is mostly in the current Croydon Central) in 1966, lost it in 1970, and was then out of the Commons until he regained Walsall North for Labour in 1979. Winnick was the defeated candidate in the 1976 by-election there, a by-election triggered by the resignation of John Stonehouse (who famously faked his own death in 1974 in order to escape from the consequences of his fraudulent business activities). Stonehouse was first elected for the Wednesbury constituency at a by-election in 1957: the defeated Conservative candidate was Peter Tapsell.
The continuous requirement stopped Tony Benn from being Father of the House himself; he lost his seat in Labour's 1983 blowout and won a by-election a few months later. Which reminds me, we're not far from his son, I believe.