Most Beatles history web sites list their TV appearances on Granada during 1962, 4 in all I think. But none seem mention who else was on the shows with them. Not surprising as they are Beatles history sites and only appearances with "major" icons of the time would probably be of interest.

Jusi to add a bit of TV historical information, AIUI, at that time Granada held the ITV franchise for the whole of the North of England, not just the North West, Mon-Fri only. They took on the 7 day a week franchise for the NW only in 1968. Only mentioned since, in 1962, their coverage area would have included Yorkshire and Lakes/Northumbria (if ITV transmissions went that far at the time) which would extend the potential local folk group possibilities.