Having that stable income is the main thing. At 18, min wage and 40hr a week you'll be taking home £1111.58 per month. It's tight but as a single person it can be done.
How much you want in the bank to make a move is inversely proportional to your desire to get out of the house! More is obviously better but I'd say £1000 at an absolute min. £1500-£2000 preferably.