The copyright in the sound recording as such belongs to the producer. Unless a contract says otherwise. This is a slight oversimplification.

A traditional song/tune/set of words will be out of copyright. But a particular arrangement may be in copyright. If it is your arrangement the copyright in the arrangement belongs to you. Unless the contract says otherwise. The MCPS and PRS may have an interest in prior arrangements that may still be in copyright, insofar as substantially reproduced.

You also have performers' rights under the Copyright Designs and Patents Act but if you have knowingly performed for recording without protest you are likely to have waived those rights - but this is more complex.

Of course if you have recorded on the basis that there would be a signed contract before exploitation then you may have effectively reserved your performer's rights and you may still be able to assert rights in your arrangements and performance - and the contract will say what it says when it says it.

A contract of employment changes things. The "work for hire" concept is not known in English law, but implied licences are known.