There are usually a number of sing-a-rounds, musicians sessions, mixed song & tune sessions at any one time. It is possible to walk around most of the venues where these might have started up in about 30 min (unfortunately the cross keys is a bit of the central circle). Many of the pubs have courtyards as well as more than one inside room. Most of them want music and/or song and will welcome singers & musicians, occasionally with a complementary drink for those who actually start a session or sing-a-round. If you don't get what you want at one place you may well find it somewhere else. And don't be afraid of starting someting with a friend or two, in years gone by some of the most enjoyable sessions in which I have participated have been ones that Lady Nancy & myself have started and we have then been joined by a good number of other musicians/singers who were into the same sort of music. I also have to say that one or two were totally ruined by occasional drunks/uke bands/or players with amplified instruments deciding to take over and play lots of their type of music. One answer then has been to move on and find another venue... there are loads.
Otley is a large enough festival with plenty of venues to cater for all tastes!