I actually own a condo and I am currently renting it out and still living with my parents (they don't mind). The rent I receive from my tenants covers my mortgage payment and condo fee, with a little extra for my pocket, which is nice. Honestly, if I was living there myself right now, I would be able to afford it, but wouldn't have much left over each month to spend on fun things I want to do.
I have a full-time job, but it's still not the greatest pay and is considered an entry level salary. I recently graduated college and have been working at this place for a year now, so hopefully I will get a raise soon. We were supposed to get raises in April but it was pushed back to July because of the bad economy and the company wanting to be cautious. So fingers crossed I'll get a raise this month. I make about $33,000 for reference. What's that equal, maybe 20,000 british pounds? not sure about the conversion rate. But yeah, it is around what you were thinking you will need to afford a place. I don't have to dress super nice and wear suits at my work. Luckily it's a laidback place and we can actually wear jeans everyday. I work in customer service (sounds scary, I know), but it is not too bad and is mostly done through email. When I do have to talk on the phone it sucks cause I have huge anxiety in that area, but I've definitely been getting better. So I don't have to be super fake and sell my soul or anything.
My big advice when looking for your first home is to look for a foreclosed property. Now, I live in America, so I'm sorry I'm not sure exactly how the foreclosure process might work in the UK, but the condo I bought was a foreclosure and it was a very good buy. Not sure how UK banks and mortgages work either, but it's very likely that you will need to have a full-time job in order to qualify for a loan. Maybe your government has some incentives out there for first time home buyers? You could look into it and check. The US has an incentive for first time home buyers, where they get $8000 back with their tax return. It's $8000 this year, but I bought my condo last year when it was $7500. Still a good chunk of change though which helped a lot.
But yeah, I'd definitely say just keep on saving, look for a full time job, and do some looking online and in newspapers for foreclosed properties. With foreclosures you can get much better deals instead of having to pay full market price for a house.