Can you not just go and get a new medical from a different Authority? I don't see how any authority can block a SOLI. Surely it's up to the new authority whether they take you or not. If the LBA won't let you go then you always have the option to surrender your LBA licence and jump through whatever hoops are necessary to get a fresh EASA licence. Have you got a CAA ATPL? There are still authorities that will give you an EASA licence based on your CAA one.