Free car check
A free car check is a lookup of the vehicle data DVLA and DVSA publish for a UK registration: tax status, MOT status and expiry, fuel type, engine size, colour and date of first registration. It is free because that data is public. It does not include anything a seller would rather you did not know.
Is a free check enough before buying a car?
It is enough to catch an untaxed or un-MOT'd car and to confirm the plate matches the vehicle in front of you. It cannot tell you whether the car is stolen, still on finance, previously written off, or whether it has ever been serviced. Those four facts are the ones that cost money to get wrong, and none of them are in the free public record.