Despite the negativity, there are lots of small/independent garages that aren't rip-off merchants and are actually genuine people. You certainly don't need to get one from a proper dealership, in fact, most dealerships don't sell older cars at lower prices - if they take an older car in part exchange, they pass it onto smaller/independent garages to sell.
You just need to know what you're looking for. I.e. a car with a full service history, check the online MOT history to see what it's failed on previously (if any) and for any "advisories", i.e. problems that aren't serious enough to fail an MOT, but are merely warnings about what may fail next time etc. You can also check mileage history from the online MOT record. Make sure the garage will provide some kind of warranty - at least six months preferably which should cover you for anything that crops up in the first few months you own it (most things do that you don't notice immediately, such as a faulty heater if you buy in Summer!). Some garages will offer a longer warranty, but not for the bargain basement type of car (i.e. under £5k). You can get cars checked over by firms like the RAC for a smallish charge, but most of what they do, you can do yourself, i.e. check MOT history and check for outstanding finance, but they sometimes include a physical check to check for undeclared accident damage or "cut and shut" etc.
You should be able to source a car that will last a few years for £5k-£7.5k range if it's got full service history and below average mileage.
You could also take a punt on a car under £5k but be prepared for it maybe not to last more than a couple of years, or be prepared to pay for repairs etc.
Today, the average car on the road is 13 years old. So that shows that you don't need a new or nearly new car. They last a lot longer than they used to, especially if driven carefully and below average mileage.
There is lots of research you can do about reliability of each type of car, what tends to go wrong and over what timescale etc.
The thing with buying older/cheaper is that you have to do more homework and take more responsibility as to what you're buying. Just educate yourself so that you don't unwittingly buy a dud.