I am 32 and DH is 30. We bought our first house (tiny 2 bed terrace, but in a nice area) 7 years ago when you could get very high loan to value mortgages. At that time I also had £30k of student debt
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We have since rented it out and bought a second house (which we live in now) that is a decent size 4 bed semi, but we needed a minimum 15% deposit for that and the only reason we could afford it is because I worked for a couple of years in the City and we were very frugal so it enabled me to pay off all my student debt in the first year and save a deposit and some extra in the second year.
We haven't had any parental help because my mum hasn't got any money anyway and DH's parents earn less than we do, so it would be wrong to take money from them (although they have worked hard and been careful and now that FIL is retired they are comfortably off and have his generous public sector pension and lump sum). They did offer to sub our deposit for our first house but we didn't want to start out owing them money.
Of the people I know who have their own places, most of them have had some sort of 'windfall' (wrong word, but can't think of the right one) - three have had inheritances (two of them inherited the house itself outright), one had a car accident that caused her to go deaf in one ear, one had her parents act as guarantors on her mortgage and one has a rich father who gave her the deposit.
There are some others who have managed alone though. One friend is a nurse but very very careful with her money and she saved very hard for several years to buy a small flat. There are a few others who have highly paid jobs who could get by without financial help from family, although some of them accept additional help anyway!
Many of my old school friends don't own their own place. I think that is fairly normal for those in their early 30s these days.