Take this opportunity to save for a rainy day, get three months wages in the bank, and then start looking to have a better life.
Gotta agree with showboat; I've just bought my first place and I'm on a touch more than you (around 24k without overtime), so again call it 1500 p/m after tax.
Luckily house prices around here are quite low (bought my own place, brand new build, 2 bed end terrace for 117k). My mortgage is around 400 p/m, factoring in all the utilities and my car I'm only looking at a couple of hundred spare, which isn't a lot. However I had a really good oportunity to get onto the housing ladder so I had to take it.
My words of advice? Don't get out right away, save like mad for 6 months, you will need a lot of disposable money when moving into your own place as how are you going to afford to buy literally everything which is needed? If you pick up an unfurnished rental place, look around your room now and count all the necessities (carpets, curtains, light fittings, tables, sofas, tables, tv etc etc etc), trust me it adds up to a lot!
It's do-able, but you need savings and you need a clear indication of how much everything is going to cost before you can even think of getting a place. I can only echo the above statements: get a spreadsheet, put everything you earn in there, write down all of your out goings and expenses and write down how much rent and utilities and food etc etc is going to cost you. Is it do-able?