I was 25 when I bought my flat.
I had finished uni in '77, got a job base in London but was immediated seconded to Edinburgh for 6 months - on expenses, so barely touched my salary of £3000. While there, I worked 9 to 5, then had computer time of 8 til midnight, so a shed load on overtime.
By the spring of '79, I had £3000 saved. I bought a 3 bed flat in London for £14000 . Took all my savings, but it was the best thing I had ever done. 5 years later moved within London, selling flat for £23000, buying house for £29000. Two years later got transferred to Cardiff, sold London house for £63000, bought Cardiff house for £48000., where I still live.
No help from parents, just a combo of long hours and a decent slice of luck.