I think both Michael Grade (BBC Controller during the classic series) and John Nathan Turner killed the series off originally.
What killed off the show originally was its failure to move with the times, for several reasons. The programme was always low budget, but for a long time that didn't matter so much - people were very forgiving (it wasn't trying to be a serious gritty space drama, it was a family show that didn't take itself too seriously) and the series was very witty and inventive in spite of its production shortcomings. Over time though, audience expectations changed, especially post-
Star Wars and the resulting boom in impressive-looking US SF. Suddenly,
Doctor Who looked terribly old-hat, and in hindsight should probably have either been put out to pasture at that point, or had a massive cash injection, but for whatever reason neither one of those things happened.
The lore goes that when Graham Williams left, the BBC had a hell of a job finding a replacement - every producer they approached took one look at the budget and basically said, "No way! I can't make it for that amount of money; a few years ago maybe, but not now." JN-T was apparently the only one who threw his hat into the ring.
The show was allowed to limp on into the '80s, still being made in the same vein as it always had been, essentially in soap opera fashion; studio-bound, multi-camera, horribly over-lit and on on a strict time limit. If the shots weren't in the can by 10pm, tough; the electricians would pull the plug. Done.
With the show looking increasingly cheap and laughable, its reputation declined and it became a poisoned chalice within the TV industry, which fed back into the quality of the show itself. This was compounded by a series of bizarre creative decisions by JN-T - Colin Baker's outfit and characterisation, not wanting to use established
Who writers etc. It was a vicious circle; Michael Grade and Jonathan Powell hated the show, and weren't interested in regenerating it, as it were; it would have cost a lot of time and money and they wanted to do other things. By now, the programme was a 20-odd-year-old relic from a bygone era, created by a previous regime with a different ethos; it was being run into the ground and they had no passion for digging it out.
After the cancellation crisis of 1985, the tabloid "outcry" resulted in a reprieve (on the condition that Colin Baker be replaced), but with the series being actively sabotaged from within by being scheduled opposite popular soap opera
Coronation Street, essentially a suicide slot. It's pretty much exactly what happened with
Star Trek Season 3.