Hi! Long time lurker here, so please go easy!

Flying BA J JFK-LON back in December I was faced with the same issue, as check-in agent told me I would not be allowed in Galleries lounge. However, after asking if we could find another solution she was kind enough to phone the Concorde Room where I was allowed to enter (go figure), because there alcohol is served by waiters (n.b. who were more than happy to bring me champagne).

Hope this helps!