One of the strange things about finance secured on assets is that the lender is not obliged to record the security anywhere, not even on HPI, Experian etc.

Realistically, the only way to discover the lender is to ask the seller or to ask the collections agent. He may cite client confidentiality, DPA or whatever but the simple fact is that you have rights to your confidentiality too and have done nothing wrong so you want to know who your private info is to be supplied to. It is important to be co-operative because that demonstrates good faith which forms part of the "innocent purchaser" defence.
I wouldn't recommend asking the seller because A) it is another contact between you both, and B) getting the info from him could suggest a link between you.

Meantime, I would get in touch with HPI to warn them that you have a potential claim under your guarantee from them and they will want to get involved to minimise how much a settlement costs them - for instance, they may choose to make enquiries to identify the lender (I'm not certain, but think they can circulate the vehicle details to lenders to see if anyone puts their hand up). Even if they can't/won't do that, by starting your claim now it minimises the time the whole thing might take to wrap up.