The BBC Proms, [...] offer £5 tickets to every
concert, if you're willing to promenade (stand).
The BBC FAQ [1] says "you always have a good chance of getting in (although early queuing is advisable for the more popular concerts)" - does "early" mean 30 minutes before the concert starts, or 6 hours before? And how do you tell which concerts will need earlier queuing?
The last time I went though I think almost everyone in the queue got in. The person who sells the tickets in the queue can normally tell you what your chances of getting in are.
My advice is to arrive 30-45 minutes before the performance, with a blanket to sit on and some snacks and just have some alternative things to do in South Kensington in case you don't get in
If you're not sure get there a couple of hours early, have a look at the queue and if its non-existant pop down to the Science Museum for a bit, or The Natural History Museum, or the V&A, they're all within 5 minutes walk of the Albert Hall, all free, and all worth the trip by themselves.
I'm not really a classical music fan but I would certainly recommend going to the Proms at least once just for the experience.
One doesn't have to stand the entire time either. Plenty of people do sit around the edges, and almost everyone does during interval. The advice to bring a blanket to sit on is good.