You will find that as the car was bought on HP, the Supply of Goods (Implied Terms) Act 1973 is the appropriate act; as it is not a 'Sale of Goods' for the purposes of SoGA '79. In particular, you need to rely on s10, whereby:
(2) Where the creditor bails [Provides] or hires goods under a hire purchase agreement , there is an implied term that the goods supplied under the agreement are of satisfactory quality.
(2A) For the purposes of this Act, goods are of satisfactory quality if they meet the standard that a reasonable person would regard as satisfactory, taking account of any description of the goods, the price (if relevant) and all the other relevant circumstances.
(2B) For the purposes of this Act, the quality of goods includes their state and condition and the following (among others) are in appropriate cases aspects of the quality of goods�
(a) fitness for all the purposes for which goods of the kind in question are commonly supplied,
(b) appearance and finish,
(c) freedom from minor defects,
(d) safety, and
(e) durability.
Obviously it is s10(2B)d that you are concerning yourself with. If I was you, I would stop by your local garage for an informal chat with a qualified mechanic, or post a form of this question in the motoring section.
If you are writing to the company, do not mention the law unless you have to. It can be very annoying to hear someone say 'I know my rights...etc' when a polite letter and rationality will have a much better effect. Of course, if it gets nasty, then bring it out.
By the way, you need to ascertain any damage that has been caused, as it may be chargeable to this company. Don't forget that for your purposes, your contract is with the HP company...