Yes having or getting proof works in your favour the more sources that can give you proof the better but remember with faults in the first 6 months of purchase you don’t have to prove the fault was there! If all the faults are still there and the garage has already had an attempt at repair then I would try push for a replacement. If you chose to write a letter recorded delivery then be sure to also mention that you have the 'reverse burden of proof' it sometimes helps in those letters. The letter is the first stage in enforcing your legal rights, first step towards court action, it makes and is the recognised way of making the complaint formal (recorded delivery and keep a copy for yourself).

The two other problems did you get back in touch with the garage in the 5 months and tell them this? Anything within the first 6 months you have the reverse burden of proof so you could possibly claim back any expenses for repairs in the first 6 month as the garage would have to prove the fault was caused by you or wear and tear. To formalize the complaint why don’t you write a recorded delivery letter (and keep a copy) to the garage and if they are a franchise their head office as well. The purpose of the letter is to enforce your legal rights so make a heading of the Sale of Goods Act 1979 (as amended) then write down what the faults are, also mention the reverse burden of proof. Tell them you want the car repaired/replaced and for a response in 7 working days. Remember the Sale of Goods Act 1979 (as amended) says your car must be of satisfactory quality, durable, safe etc (also bear in mind the mileage and age of the car) If that fails get in touch with your local Trading Standards as some of them act as arbitration scheme for civil law issues. Find out if the garage belongs to a motor association as most of them have arbitration schemes.

If debit card then you will be covered by the Sale of Goods Act 1979 (as amended) which says your contract is with the garage you bought the car from, but because you have had it for over 6 months you would first have to prove a manufacturing fault or defect. Your warranty and your statutory rights are two different things, even if your warranty runs out you are still covered by your statutory rights (for 6 years in England). You might need a fully independent report. If the 'squealing from the wheels and a kangarooing under acceleration' was not fixed first time and it's still there you could push for a like for like replacement car.

How was the £2000 paid? in cash, credit card, debit card, trade in, finance and if so what type? HP, Fixed Sum or conditional? Due to owning the car for more than 6 months you would have to prove there was a manufacturing fault with the car first of all by independent report(s). Once proved you have rights against the garage, but what bit of law applies depends on the payment method? So how did you pay?