Depends what and where you are, Jessiadel. As a british citizen living in DC (also a US citizen), it took me all of four days once I turned my application into the Embassy here in DC. I know that last year, though, the Home Office was having incredible delays in processing domestic applications (like months and months). It was something of a crisis, and I expect it has been addressed by now, I think.
If you're talking general immigration, though, I'd expect about, oh, forever