I live a few miles from Brighton, and I'm chuckling at "10 miles isn't too far if you have a car".
Brighton grinds to a halt in morning and evening rush hours, an accident on any of the main routes out of town causes gridlock for miles around and parking is so exorbitant that I've heard of someone renting out their parking space, a short walk from the station, for £300 a month! DP gets the bus to work, and there have been a couple of times it has taken him 2 hours to get home because there have been accidents on the A27.
You're right, OP, it's shite. Rents are ridiculous and letting agents are vultures in the fees they charge. And people are having to move away from their home towns right across the area, it's not just Brighton.
Housing is in a ludicrous mess in this country, at least in the south. If you can get a deposit together and earn enough, you can buy a flat with a 10% and your mortgage can be significantly less than the rent you would pay for an equivalent property. If you don't earn enough, you're stuffed, paying nearly half your combined income in rent.
Having said that, my DGDs mum found a 2-bed for £950 a short while ago. It has no garden, and is on a busy road (Elm Grove), but the flat itself is nice and in good nick.
I've known people find places through FB, by getting in quickly when people they know are moving out etc.
And don't give up on the council. There's a lot of new building going on, most with some social/affordable housing, and Brighton council restricts a proportion of lettings to the "economically active", ie working. Keep looking, and keep bidding.