In reply to samparsons:
Berdorf no longer has a permit system but as you say you need to be in a club that has reciprocal rights ie. affilated to the UIAA or IFSC
I think normal BMC membership does not have reciprocal rights - you have to pay extra
Also maybe have a look at Austrian Alpine club as they have a UK section
I don't know how rigorously they check people's cards