Although it is true that having another class 1 will carry some weight this is likely to be the case only if you have actually flown something which required a class one. Just being able to wave the paper bit is unlikely to be a magical want.
Rather than forking out for an FAA or other country's medical I do think that you best ring the CAA and see what they say.
If that route does not work and you are desperate to fly for a living you can always see if you can pursuit a career under a different licensing authority.
As I said in my opening reply, it will very much depend on what your 'problem' is.
Contrary to popular belief non JAR medicals are not a cure all for all ailings and the CAA's point of view may well be shared with other authorities.
FD