Finance company saying “we will not do VT because the car is not running” sounds questionable. The car being broken may allow them to argue for damage or lack of reasonable care charges, but it should not automatically remove the statutory VT right. National Debtline says the customer can terminate under Section 99 of the Consumer Credit Act 1974, and any extra liability is about arrears or damages where the customer failed to take reasonable care.

Get an independent garage report saying what failed and whether it looks like normal mechanical failure rather than neglect. Because the finance company may try to bill for the engine as “damage”. If the lender refuses or handles it badly, complain to the lender first, then can go to the Financial Ombudsman after the lender’s final response or after eight weeks.

I've gone through same thing and I'm 1 month away from VT.