Unless you will begin a modular CPL training course before Implementation Period completion day (31 Dec 2020
*) it hardly seems worthwhile changing the state of licence issue now. This is because
any ICAO Annex 1-compliant PPL is sufficient to commence the modular CPL course.
See Part-FCL appendix 3 section E in the current consolidated EASA Aircrew Regulation (
link):
E. CPL modular course — Aeroplanes
GENERAL
...
2. Before commencing a CPL(A) modular course an applicant shall be the holder of a PPL(A) issued in accordance with Annex 1 to the Chicago Convention.
...
You may also begin the Part-FCL ATPL theoretical knowledge course as the holder of an ICAO Annex 1-compliant PPL. After IP completion day when the UK will no longer be an EASA member state you may concurrently hold a UK Part-FCL PPL and an EASA Part-FCL CPL.
Numerous UK-based training organisations will be approved by EASA after IP completion day. A list of these is published near the bottom of the EASA ATOs webpage (
link — or navigate on
www.easa.europa.eu to
EASA Pro -> Domains -> Aircrew & Medical -> Approved training organisations).
In foregoing a change of SOLI now I expect you'd be required to undertake another initial Class 1 medical later. Centreline Aviation Medical Services, which appears on that list, can advise.