Nowadays there are (or at least should be) performance royalties for session musicians in the UK this is administered via PPL. It wasn't always the case , for instance Vic Flick as paid the standard session fee (£6 or so at the time) for playing the guitar riff on the James Bond theme.

If a session player contributes something that becomes an intrinsic part of the composition, he or she may be able to argue the case that they deserve some of the writing royalties, providing they had actually made up the part, and not signed off any further claim in the work. Otherwise it would come down to the lawyers.