The extant TOTP clip of Don't Make My Baby Blue from the summer of 1965 dates from before the BBC's (and ITV's) 1966 decision not to allow miming to commercial records any more and is therefore an "official" miming performance to the single.
The group were all "playing" their Burns guitars and were all clad in dinner suits (tuxedos) and bow-ties.
As mentioned a couple of lines above, it wasn't only the BBC which adopted a "no miming to records" policy in 1966. The ITV network did the same, though that really only had a big effect on Rediffusion's "Ready, Steady, Go!" and on whatever regional programmes the other contractors did locally.