Dont get a new car. Its price is cut by 1/3 the minute you drive it out the garage. £2250 would get you a decent car, i.e Hyuandai i10 with 50k miles. If your parents dont mind, the best option would be to slowly pay your parents back for a used car.
However, you have to consider insurance is stupid and if you want to get a black box that wont be possible if you share a car.
So personally I would buy a used car in a low insurance bracket, get a black box and over time you'll save on insurance.
An example,
https://www.autotrader.co.uk/classified/advert/201808159532873?advertising-location=at_cars