Probably 10/05/1964 and 05/10/1964 are all that's left in the BBC archives, but I'm pleased we have some representation of this music programme, as we get to see The Kinks, Tom Jones and The Beat Girls.
My apologies. I think you're right in saying Tom Jones is in the same show as the Beat Girls and the Kinks.
I've since realised why I listed the BBC as having two editions. One source listed the same date the other way around, eg 05/10/1964 (the correct date) and 10/05/1964, the American date order. After reading your reply, it occurred to me this is what had happened.
Thanks for the link. Those photos correspond with the footage in the 6 links to the complete show, starting off with Tom Jones - What'd I Say:
http://www.youtube.com/watch?v=2ChuXGdqeaY - Rosetta Stone cover featuring Ian Mitchell of the Bay City Rollers as I think lead singer - A TOTP performance exists somewhere (not at the BBC) of this from 08/09/1977, but has yet to surface online in addition to Black Gorilla's Gimme Dat Banana:
left to right Babs Lord , Lorelly Harris , Dee Dee Wilde , Diane South and Penny Fergusson
5 September 1966
The Beat Girls , from London's Dance Centre near Covent Garden overjoyed by the news that they are flying to Venice to support entries in the Venice Film Festival photographed outside the Lamb and Flag pub in Covent garden , London 5 September 1966