If a car is registered in my name but I don't own it, are they still allowed to take it?

No

Bailiffs may take control of goods only if they are goods of the debtor.^[1]

The registered keeper on the V5 is not the owner of the vehicle.^[2]

^{[1] Paragraph 10 of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007
[2] See Is the V5 proof of ownership of a vehicle?}