Your medical records are always held by the State that issues your licence.
Are you sure that is currently also the case with class 2 certificates, and not only with class 1?
See:
How to obtain a UK JAR Licence if you hold a non-UK medical certificate/licence | Medical | Safety Regulation
There they state they do want the medical records (last application form, examination form, ophthalmology if indicated and copy of last ECG and Audiogram) if it concerns a class 1.
But all I had to sent them when I applied for the UK JAA PPL, was a photocopy of my Dutch class 2 certificate.
The UK currently doesn't have my full medical records as far as I'm aware.