What Conditional sale means for you
For a buyer, the car may still belong to a finance company when you first see it. The V5C logbook shows the registered keeper, not the legal owner, so it won't reveal outstanding finance on its own. Ask the seller for proof that any finance has been paid off.
If you buy privately and in good faith, a conditional sale usually still gives you good title under the Hire Purchase Act 1964. That protection doesn't cover dealers or logbook loans. A Finance & Stolen Check costs £4.99 and is worth doing before you pay.