No, AnthonyDunn, at both LGW and LHR bags from international (non-EU) destinations can be checked through to domestic destinations in the UK and are then delivered on a separate belt on arrival (at least in GLA). International to domestic transfer at LGW is a pain and has been commented on before – I guess the volume is relatively small and not deemed worth the establishment of a dedicated route with UKBA facilities etc?
Personally, I really like the BA First Lounge in Gatwick – quirky and old fashioned, maybe but generally quiet and there are limited hot options on the menu too.
EDITED TO ADD: Never had problems with the Priority Channel either – usually very fast and the folk there are polite. Even when it is closed, the alterbative priority route through the main entrance works well in my experience.