There are in fact two queues for arena tickets. One for season ticket holders and one for everyone else (ie: me and probably you too). The season ticket holders get to buy their tickets first and then *if* there is still more room, they start letting in everone else. But I've never heard of people not getting in . I'm sure they run out of room eventually- but I've never actually witnessed this.... In any case, my raffle ticket was No.68, my actual ticket was No. 467 and I remember reading somewhere that they have about 750 tickets up for grabs.
What I'm trying to say here is that you should make the effort to go if you happen to be in London at the begining of September. I'm sure every Brit knows about it but thinks it's too difficult or expensive to get into the Hall- which is fair enough considering it already costs £25 to go see the Last Night in Hyde Park, which isn't even the "real" thing. On the other hand, most foreigners who aren't in tune with the goings-on of the classical music world won't even know what the Proms are!
The Proms are the world's largest classical music festival, running from mid June to mid September every year, culminating in the famous Last Night which usually features some of the newest, best and/or most promising classical musicians in the world. And if I had access to Youtube I would now link you to videos of last year's proms, featuring the gorgeous and hilarious opera singer Anna Netrebko.
The Last Night of Proms might be the most patriotic event I've ever attended and even though I'm in no way British (in fact my American and French blood quite possibly makes me the opposite of British) you can't help but wave your union jack, learn the melody to "Jerusalem", sing along to "Rule, Britania!", stomp along to the sailor's song and shake hands with your neighbors during "Auld Lang Syne" at the close of the night. I'd say it's really something worth seeing at least once.