How long can a vehicle on Hire Purchase remain clamped?

It can't

Goods on hire purchase, leased, personal contract purchase, cannot be clamped, let alone removed, because bailiffs may only take control of goods that belong to the debtor.^[1]

Any car or vehicle on hire purchase remains the goods of the lender until the final payment has been made.^[2][3][4][5]

If the bailiff clamps a car on hire purchase of any length of time, the hirer, or driver, may sue for damages,^[6] and apply to the court for interlocutory relief (an injunction).^[7][8][9]

The hirer or driver may also recover costs.^[10][11][12]

^{[1] Paragraph 10 of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007
[2] Chitty on Contracts (32 ed.) ss39-307 paywall
[3] Mulwanyi v London Borough of Croydon and Newlyn Plc, Central London County Court, 7 Apr 2017
[4] Opinion by John Kruse Bailiff Scholar
[5] Tandea v Marston Group Limited, Central London County Court, Jan 2020
[6] Section 3 of the Torts (Interference with Goods) Act 2007
[7] Section 4 of the Torts (Interference with Goods) Act 2007
[8] Paragraph 66 of Schedule 12 of the Tribunals Courts and Enforcement Act 2007
[9] See Making a claim for clamping or taking a car on hire purchase
[10] Civil Procedure Rule 44.2
[11] Civil Procedure Rule 46.5
[12] Practice Direction 46. Rule 3.1}