While the Cathy Gale episodes of The Avengers, which date from around 1962-1964, weren't live, they were shot in studios in a multi-camera environment, often "as live" to get through it. They weren't necessarily filmed either, with many first season episodes still missing as the tapes were wiped (as with Doctor Who). But that meant that while sometimes the sets creaked a little, Blackman herself had to do most of her own stunts, with no opportunity to switch out a stunt double.
It was only after Honor Blackman left to make Goldfinger, and Diana Rigg joined as Emma Peel, when the British "ABC" (Associated British Corporation) sold the series to the US "ABC" that the move was made to film. And from the second Emma Peel season, to colour. Indeed ITV who broadcast it in the UK didn't move to colour for another three years, so only US audiences saw it in colour!
I dug out my DVD boxset of the complete series last night for a third season episode from the peak Honor Blackman era.
RIP