Who actually owns the car?
This is the most common misconception in the used car market. If a car is on finance (PCP, HP, or a Logbook Loan), the finance company is the legal owner, not the person selling it to you.
Until the final penny is paid, the driver is merely the "registered keeper" on the V5C logbook. Being the keeper does not mean they have the right to sell the vehicle.
What happens if you buy a car with finance?
If you buy a vehicle that has outstanding finance attached to it, you do not obtain "good title" to the goods. Essentially, you have bought stolen property.
If the seller stops making payments (which they often do after taking your cash), the finance house will track the vehicle down. They have the legal right to repossess the car from your driveway. You will lose the car and the money you paid for it.
Does the "Innocent Buyer" protection apply?
There is a legal clause called "Good Title" (Section 27 of the Hire Purchase Act 1964) which might protect you if you genuinely didn't know about the finance. However, proving this in court is difficult, expensive, and stressful. The finance company will fight hard to get their asset back.
How to check before you pay
It is impossible to tell if a car has finance just by looking at the V5C logbook. Finance data is held on a separate database shared by banks and lenders.
Essential Check: A standard £3 vehicle check usually excludes finance data because it costs more to access. Make sure you purchase a "Full" or "Premium" check that explicitly includes a Finance Check.