I see no valid reason why the DfT/UKCAA shouldn't permit G-reg Part21 aircraft to be flown in UK airspace with a UK-issued licence.........
Why such a restriction? Remember, there are no longer "EASA aircraft" registered in the UK. Subject to ICAO a UK registered aircraft may be flown anywhere in the world including the EU, when the pilot holds a UK ICAO compliant licence.
The OP can only be advised by an AME with regard to his medical history and current medical compliance. This advice needs to be obtained before any licence options can be considered. If all goes well and a Class 2 medical is regained then the expired JAA compliant licence will be reissued as a ICAO compliant UK PPL. There are too many ifs and buts until the medical is resolved.