Can a bailiff take a car that’s only insured by me?

No

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

Being insured on a vehicle does not confer title over it.

If a bailiff takes a car that does not belong to the debtor, the owner can make a third-party claim.^[2][3]

The owner also has a right to recover damages for the loss of the use of the car,^[4] together with his costs of bringing the claim.^[5][6][7]

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