Various comments on the above:

1. These days, a keyboard does not have to be a piano. Good portable keyboards are available.

2. The PRS only has control over music which is in copyright

3. The PPL ditto over prerecorded music

THEREFORE
a) A privately recorded CD containing only non-copyright material AND/OR material written and recorded by the vendor
CAN be played in a pub without a PPL licence

b) provided the premises has a licence for entertainment, it can provide live performance of TRADITIONAL and self-penned material without paying the PRS.

Therefore it becomes more economically viable to provide folk, classical and early music than pop, rock or jazz.

The biggest problem is in determining what is in copyright - see many other threads. Even if a song is not in copyright, the tune or arrangement may be.

In particular, you cannot even sing 'Happy Birthday to you', because it is still in copyright.