I made this list for a comment a couple of months ago but as I've seen it brought up in some places since, especially given the announcement BBC4 are continuing on to 1977, it may be worth bringing it to a proper audience. Although conventional British pop history has it that punk was born in 1976 and revolutionised the whole country the following year, it's a music press fallacy to some extent. There were no punk singles until late October 1976 and certainly it was something largely being chased up by a faction within the music press - the Sex Pistols were on the NME cover dated 2/10/76 but only as an adjunct to then-supposed fellow travellers Dr Feelgood, while in the first half of 1977 there were as many covers featuring Dolly Parton and Genesis as there were the Clash and Damned, while the five covers from July of that month, according to Wikipedia, mix 'Murder at a punk festival' and 'Anti-Punk violence' with Frankie Miller, Steve Harley and Nick Lowe. And when they did go for it they put the MC5 on the cover twice in seven weeks despite that band having been inactive for nearly five years.
In our little prime-time enclave certainly initially there was little appetite yet for getting pissed and destroying. The record buying public continued on their way unhindered - David Soul, Leo Sayer and Brotherhood Of Man all appear in the year's ten best selling singles - and given not so long before then punks were being seen as a credible threat to the national way of life it's not like TOTP was going to bend to their will, especially with the Clash refusing to appear, the Damned briefly fizzling out (Music For Pleasure got bad reviews and they split up for a year or so), the Buzzcocks either considered too independent (Spiral Scratch) or too banned (Orgasm Addict) and the BBC in general still unsure about which way this was all heading. 1978 and 1979 was very different in booking terms, but we'll get there in time.
As such, here's a cut out and keep guide to all the punk-affiliated TOTP appearances in 1977:
19/5/77 The Jam - In The City
26/5/77 The Stranglers - Go Buddy Go (the other half of the double A side that featured the banned Peaches)
14/7/77 The Saints - This Perfect Day; Sex Pistols - Pretty Vacant (video)
21/7/77 The Jam - All Around The World
4/8/77 Television - Prove It (don't wait up for this, as far as we know it's been wiped)
25/8/77 The Adverts - Gary Gilmore's Eyes
1/9/77 Elvis Costello - (The Angels Wanna Wear My) Red Shoes
15/9/77 Generation X - Your Generation,
22/9/77 The Stranglers - No More Heroes
27/10/77 Tom Robinson Band - 2-4-6-8 Motorway; Sex Pistols - Holiday In The SUn (under the credits)
10/11/77 Elvis Costello - Watching The Detectives
3/11/77 The Jam - The Modern World
8/12/77 The Banned - Little Girl (already onto the cash-ins, here members of prog third-raters Gryphon chancing it)