The UK used to have a scheme somewhat similar to the USA's compulsory licence for re-recording copyright works. It was under S. 8 of the Copyright Act 1956. It no longer exists and there is no similar scheme under current UK law.

It applied to a work or adaptation of a work and permitted the recording of that work or a similar adaptation and thus did not cover the making of material alterations.

If the MCPS administers a work it may be possible to get a licence to record that work from them. The standard MCPS licence does not permit the making of substantial alterations to a work and some at least MCPS members reserve the right of first recording so that no MCPS licence to record the work is obtainable until after the first recording is made with the prmission of the copyright owner or his licensee.