Yes
The bailiff may only take control of goods that belong to the debtor.[1]
Registering a name of a person as the vehicle keeper with the DVLA does not pass title to them.
If the debtor is named on the warrant, the bailiff may take control of goods owned by that debtor, irrespective of whose name is the registered keeper with the DVLA.
If you want to insulate yourself from liability from traffic contravention debts or you are working in an occupation that is hazardous to attracting traffic contravention penalties, for example, a cab or a courier driver, then the vehicle must be owned by someone other than the registered keeper, and evidence of the flow of money for the purchase of the vehicle must be given in evidence.
If bailiffs attend for an unpaid contravention, debt and take control of the vehicle, the owner makes a third party claim on the vehicle,[2][3] and he may also recover costs,[4][5][6] and damages.[7]
[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
[4] Civil Procedure Rule 44.3
[5] Civil Procedure Rule 46.5
[6] Practice Direction 46.5 Rule 3.1
[7] Section 3 of the Torts (Interference with Goods) Act 1977
Protect your car from bailiffs | Recover Your car from bailiffs | Attending a bailiffs vehicle pound | Reclaim bailiffs fees | Getting a chargeback | Attending Court | Arrested? | Bailiff Law | Your bailiff FAQs | National Bailiff Advice | Beat the Bailiffs | About Stop the Bailiffs