I am the registered keeper, a family member is the legal owner can bailiffs take his car?

No

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

The Local Government Ombudsman, Focus report: learning lessons from complaints, states:

We consider that bailiffs should check the vehicle does belong to the debtor before removing it.^[2]

The registered keeper of a car is not the owner.^[3]

^{[1] Paragraph 10 of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007
[2] Local Government Ombudsman, Focus report: learning lessons from complaints
[3] See Is the V5 proof of ownership of a vehicle?}