Can bailiffs enter my house with a warrant of control if I owe an unpaid parking ticket with the added fees?

Yes

Bailiffs can enter homes to recover an unpaid traffic contravention debt.

But, the bailiff cannot enter using force,^[1] or violence.^[2]

^{[1] Paragraph 18(a)(1)(d) of Schedule 12 to the Tribunals Courts and Enforcement Act 2007.
[2] Paragraph 24(2) of Schedule 12 to the Tribunals Courts and Enforcement Act 2007.}