Can bailiffs take a car that is not in my name?

Yes

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

The registered keeper of a vehicle is not necessarily the owner.

The owner of a vehicle is the person who can show the flow of money that bought it, or had evidence they acquired it on a date before the enforcement power was issued by the court,^[2] or the Notice of Enforcement was given to the debtor.^[3]

If bailiffs take control of goods that do not belong to the debtor, the owner can make a third-party claim,^[4] and recover costs,^[5][6][7] and damages.^[8][9]

^{[1] Paragraph 10 of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007
[2] Paragraph 4(2) of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007
[3] Paragraph 4(4) of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007
[4] Civil Procedure Rule 85.4
[5] Civil Procedure Rule 44.3
[6] Civil Procedure Rule 46.5
[7] Practice Direction 46.5 Rule 3.1
[8] Section 3 of the Torts (Interference with Goods) Act 1977
[9] See Making a third-party claim to controlled goods}