At my club in London we have the club table (seats 24) set aside for those who are dining alone. It's an interesting way to meet people from time to time and you can bring a book down from the library or get your e-reader out if there is no one else. You can't introduce non-members unless no one at the table objects.
Usually clubs require that 2 (or more) people introduce you. This can be difficult to establish.
However, my club in London is the Oxford & Cambridge club which is typically very easy to get into if you have matriculated at either of the universities.
