Thanks, Aviator Frank, Ted and Glenn! It's what I thought, that it wasn't Peter. But the caption said so, so I thought that I might be wrong (in fact, it said "Young Peter Falk"!). I hadn't heard about Richard Bradford before, but I've looked him up on the net, and it's certainly him.
Yes, this is definitely Richard Bradford who is probably best known (certainly in the UK, anyway) for his 1960's series Man in a Suitcase. He played the part of McGill, an ex US Spy turned Private Detective. It was a great series and made by most of the same people who had made Patrick McGoohan's Danger Man, by way of a Columbo connection!