Can You Get an MOT Without a Logbook?
Yes. You do not need the V5C with you for an MOT. The logbook records the vehicle and the registered keeper. It is not proof of ownership. What it contains is covered in the V5C logbook guide.
What the centre uses
The test is tied to the registration number. The V5C shows make, model, year and the registered keeper, but it does not have to be handed over for the test to go ahead. If the registration on the car does not match the record, the centre may not be able to log the test.
New keeper or a lost V5C
You can still have the MOT if you have just bought the car and the V5C has not arrived, as long as the vehicle is registered. Order a replacement from the DVLA if the logbook is lost. The MOT and the V5C are separate. This site does not update the logbook.
The MOT check shows test history for the registration. It does not book a test, and it is not a copy of the V5C.