Luck!
I bought a flat in 2002 when I had just turned 22. I had a reasonably decent job in the City and a deposit saved by taking full student loans and also working part time and during holidays whilst at uni.
I bought a tiny 1 bed flat for £118,000, put down a 5% deposit.
It was a necessity though really, my parents split when I was in my teens, our house was sold when I was 18 and my parents each bought tiny flats from the proceeds so I didn't really have anywhere to go! I was encouraged to buy rather than rent. I always overpaid my mortgage where possible.
My DH bought an equally tiny flat at around the same time and overpaid his mortgage too. We had just met.
Both flats were in London/ south east.
We both sold in 2007/2008 at pretty much the peak of the market and rented for a while together. Back in those days, for a while at least, the interest received on the savings paid a good chunk of our rent.
I made about £30k on my flat and had overpaid about £10k, my DH had virtually paid off his mortgage and so when we came to buy in 2010 we had a very good deposit for our first house together.
Neither of us got parental help. We are now 34 and 38 and have a small but lovely house in a nice part of London.
However, we couldn't afford to buy this house now (prices have increased by around a third since 2010) and many of our friends are trapped renting.