Can bailiffs take an Unregistered car I use?

No

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

Having the use of a car, or hiring a car does not assign a beneficial interest in it, therefore the bailiff may not take control of it.

If a bailiff takes control of a car that does not belong to the debtor, the owner may apply for a third party claim.^[2][3]

^{[1] Paragraph 10 of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007
[2] Civil Procedure Rule 85.4
[3] See Making a third party claim to controlled goods}