Can bailiffs take a vehicle which has my own clamp?

Yes

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

Taking control of a vehicle with a wheel clamp already attached only presents problems when the bailiff comes to sell the vehicle to pay the debt.

If the bailiff breaks off the wheel clamp, he may be liable for the damage caused to the clamp,^[2] and any defence that he had lawful excuse^[3] to break it off could fail, because the bailiff is liable for the care of controlled goods while it is in his possession.^[4][5]

The bailiff has no realistic intention of taking and selling the attached wheel clamp, so the debtor could pursue a claim for breach of the regulations rewarding the care of controlled goods, by bringing an action to recover that damage or replacement cost of the wheel clamp.^[6]

There are more practical ways to protect a vehicle from the effects of bailiff action.^[7][8]

^{[1] Paragraph 10 of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007
[2] Section 1 of the Criminal Damage Act 1971
[3] Section 5 of the Criminal Damage Act 1971
[4] Paragraph 35 of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007
[5] Regulation 34 of the Taking Control of Goods Regulations 2013
[6] Paragraph 10 of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007
[7] See Stopping bailiffs taking your vehicle
[8] See Ways to protect your vehicle from bailiffs}