Nothing wrong with a 10-15 year old car IF it's relatively low mileage, has a decent service history/MOT history to prove mileage, and it looks it decent enough condition. If there's no service history, then walk away as you'll never know what work has been done (i.e. timing belt and other "big price" things that could cost a fortune or do damage).
Don't assume local "used" car lots on an industrial estate are dodgy. Find some that are long established and go have a look at what they've got. Get them properly checked out by an RAC/AA inspection, get a warranty.
Look at the internal condition - a genuinely looked after relatively low mileage (for it's age) car will look OK inside. Excessive wear and tear of the seats, gear stick, controls, etc., could indicate it's been used more than it's recorded mileage!
For that kind of age, I'd be looking at a simple, basic model of car, without all the bells and whistles, as the more "gimmicks" you have, the more can go wrong and the more expensive to repair. So go bottom of the range model. Nothing with turbos, intercoolers, etc., and certainly don't go for any "prestige" makes like BMW which cost a fortune to maintain at that age!
Personally, I'd be looking at a 10-15 year old Citroen C3 which is a 4 door small family hatchback. You still see 04-09 plate ones in pretty big numbers out on the road. We've had 3 and still got an 08 plate one that's literally never been any trouble at all so we keep it as a "spare". It went into a private bodyshop to have a few scratches and dents repairs and the bodyshop guy offered to buy it from us for £2,500 as he was looking for a new courtesy car for customers and had had a few C3s in the past and said they were reliable and cheap/easy to maintain!
Auto trader has quite a few at the moment
https://www.autotrader.co.uk/car-search?advertising-location=at_cars&make=Citroen&maximum-mileage=50000&model=C3&moreOptions=visible&postcode=LA4+6SE&sort=relevance&transmission=Manual&year-to=2008&polaAffiliate=isis&utm_source=RoEye&utm_medium=Affiliate&utm_campaign=HELP&utm_content=Skimbit%20Ltd.&utm_term=Performance