There should be plenty of time for the connection if you're in First or Club - but being down the back might cause a problem. Chances are the luggage will take longer than immigration. If you want to skip the immigration queue I've used www.platinumservicesbgi.com before who will walk you through the 'home'/crew channel - especially useful if other flights are landing at the same time.

Have a word with Platinum Services, they may be able to collect and transfer the luggage for you while you sit in the lounge drinking rum punch!