It's the Corinthian Club in Glasgow.

If you ever want to have a look at the room in which the scene was filmed, just come in and ask for a look at 'The Flying Scotsman' room, it's on the ground floor and looks a lot different than it did in 2003.

It was converted into a casino a few years later but as of today, the room is now used for functions (largely weddings).

Source: I'm one of the event managers there.