I echo many suggestions here but will throw in this lot off the top of my head...
The Kinks on Julie Felix's show in early 1969
The Blue Peter archive from 1964 to 1966 - let's see complete songs by The Searchers, Pinkerton's Assorted Colours, Brian Poole's "I Want Candy" and The Bonzo Dog Doo Dah Band - I can't remember who else appeared on the show during that era but do recall when Infax was online there are quite a few interesting musical performances in there
Julie Rogers performing "You're No Good" - annoyingly chopped out from The Beat Room repeat
Yardbirds "Over Under Sideways Down" from A Whole Scene Going
Bonzo Dog Doo Dah Band - Noises For The Leg (a Bob Pratt saved clip from December 1969 in colour)
Anything by Alma Cogan
Dave Clark Five - Everybody Get Together from 26-2-70 TOTP
The Shadows - The Frightened City (Crackerjack 1961)
Probably too fragmented but any glimpse of The Swinging Blue Jeans on Z Cars in December 1963
Petula Clark - the BBC must have something of her in the 60's or early 70's
Cliff and The Shadows on Billy Cotton Bandshow in 1962
Jake Thackray - ok, not a hit act, but the BBC have a whole host of performances never repeated
from the 60's and early 70's
The Brook Brothers on Pops and Lenny, 1962
Herman's Hermits in December 1970... some kids show on colour VT I believe can't remember the details but know it's there unrepeated in the archive
Honey Bane - Turn Me On, Turn Me Off - TOTP January 1981... sure, was repeated on UK Gold in the mid 90's but never on TOTP2 and would be great to see in best quality
Gene Pitney - That Girl Belongs To Yesterday TOTP 1964