I go all time to the kitchen and ask for Champagne instead of asking the waiter to bring me one.
Much faster and staff never had an issue with that - I always warn them that I'll come at least 5-6 times which gives them always a good laugh. Also I have seen it many times that other guests observe what I am doing and approx. 5 min later 10 people ask for Champagne (mostly husbands who need to bring Champagne to their wives who have seen me
How they manage to provide a 'help yourself' service at Gatwick but not at LHR (I would assume guests flying on their way to holidays drink even more, but clearly not an issue) is definitely another discussion.