I agree with quite a few of the opinions above. The place is far too stuffy - and I speak as someone who doesn't mind putting a tie on to go into the Mess bar, even when I was 'living in' over the years.
For example, I stayed in London a couple of years ago to watch some rugby and invited our US exchange officer to come along. He thoroughly enjoyed the experience, and the history of the place, until he innocently made a very discreet, quiet call on his mobile phone in the foyer. No-one else was anywhere within earshot. The staff reacted as if he had exposed his private parts and abused the Queen whilst dancing around the dining room. I completely understand how mobiles can be a pain, but in this case it was a totally unnecessary fuss about nothing that showed us in a bad light. The dress code is also far too restrictive at weekends.
Other similar clubs are not nearly as retentive. The Marine Memorial Club for example, in San Francisco, is far more welcoming, even to 'foreigners' like us. The RAF Club could be a great place to stay but, as Spike Milligan would have said, it is like an inverted cemetary - the stiffs are above the ground. Last time I stayed, my wife refused to take breakfast in the Club because of the intimidating atmosphere. I have thought about quitting but I am probably too stubborn.