An allowance should be paid whether you spend the money or not so you should not feel an obligation to spend it all.
You can get an idea of insurance costs using the red "insurance" tab at the top for a quote or two. You will need to phone up to find out if the letter of no claims is worth anything. One or two insurers might recognise it.
The two main costs of running are car are usually the depreciation and the fuel. You can reduce the former by buying an older car and you can reduce the latter by getting a vehicle that doesn't run on petrol (i.e. diesel, LPG or electric). The costs of repairs depends more, in my view, on where you go than on how old the vehicle is. I recently had my gearbox replaced for £150 and some people would spend that on an oil change and a set of wipers at a main dealer. When there's a problem, many garages will tell you that there might be a fault with the over-axle exhaust olive and, if that brings a serious, woried look to your face, they will know to present you with a suitably serious, worrying bill.
If you are looking at finance, you should look at a personal loan as well as dedicated car finance and you will need to decide if any saving with the latter is adequate compensation for the inflexibility.
Before you buy anything though, you should have a look at a few web sites giving advice on how to inspect a vehicle. Any car purchase is a risk and my advice for a first purchase is to risk no more than a few hundred pounds on something less than 10 years old through a private sale from a seller who has owned the car for a while and who appears to have looked after it. There are plenty of vehicles to browse in your area on autotrader.co.uk. Don't buy the first one that you look at.