London rents are astronomical unless you live right in the inconvenient outskirts or in some grotty hole, so it's good that you're looking at other places. I've never been to Birmingham before but as it's a big city I'd imagine you'd be in a similar situation rent-wise to London and most people tend to be quite derogatory towards it as a place to live.
It doesn't have a good reputation here. I wouldn't recommend Eastbourne, either, just because it isn't a very 'young' city.
If you were moving here, the cities/towns I would recommend would be Brighton (still quite expensive, but nice), Leeds, Bath, certain bits of Manchester, York, Oxford, Cambridge and also Edinburgh and Cardiff are very nice in my experience, too. It might also be worth exploring some smaller towns if you're interested in getting more of a change of scene from Brisbane.
From my own experience, I would avoid: Newcastle and the North East (hardest to find work), Portsmouth, Plymouth, Hull, Slough (My God, stay away from there), Leicester, Stoke and Milton Keynes.