I was suggesting this more for sites like hulu, but when I try the numbers it's actually not unrealistic.
3 pounds is roughly $4.40 USD. The cheapest EC2 instance is $0.10/hour, which would give you 44 hours for that price.
I don't know what bitrate last.fm streams at, but assuming it's 128 kbps, 44 hours would be about 2.5 GB transfer, or $0.25. edit: actually, $0.50 because the data goes in and out of the servers. I'm going off the top of my head here, but I think the rate is $0.10/GB
I figure I've listened to about 65 hours of music in the last month, so if I replaced half of that with last.fm (For example, I can't use last.fm from the gym), I'd come out ahead.
Of course, it wouldn't be worth the hassle for last.fm (killing and starting instances every time you want to play music? not for me). I may try it with hulu though, just for fun.