What are the laws concerning businesses i.e. showrooms, broadcasting...

[the critical umbilical]

...'internet' radio to the public...? on their premises.

[Michael H]

you cannot do it without a licence from the PRS

Thier website has all the details for you.

This page in particular will help:
http://www.mcps-prs-alliance.co.uk/playingbroadcastingonline/music_for_businesses/Pages/default.aspx

The source of the music ( internet / phone / arial, cable etc ) doesn't matter.