If you are looking to buy a cheap used car then you may find many that only have a few months MOT left on them. These cars are often advertised with 1-3 months MOT but if buying from a garage they will often MOT the vehicle for you if you agree to buy it. If you want to get a good chunk of money knocked off the car sales price then you can agree to buy it with little or no MOT. You need to be aware that if you choose to do this you may have to fork out for repairs almost immedialty after you have purchased the vehicle. Once you have purchased the car take it straight to a garage to give it the once over. If it turns out that the car needs a lot of repairs that will cost more than the car is worth or the car is dangerous then you may be able to hand the car back and get your money back. This may not be a simple task though so you may have to go to court to fight it.
If you do buy a cheaper vehicle then it may mean that you have spare money to spend on repairs. If your budget is £1500 and you can find a car for £1000 then you can afford to spend £500 doing it up. This is better than spending your full £1500 budget on a car that still may require work to be done to it but you have no funds to spend on it.