Can a bailiff force entry to my home for a personal tax bill to HMRC?

Yes

Bailiffs collecting unpaid tax owed to HMRC may enter using reasonable force.^[1][2]

But this is rarely practiced, because it doesn't always recover the money owed, and causes damage to the property, which the cost usually falls on the local authority or landlord.

The threat of breaking and entering homes is to coerce payment, rather than cause damage to people's property.

Debt advice charities sponsored by the taxpayer, such as Citizens Advice, StepChange and National Debt Line construe that entering using reasonable force means breaking and entering.

^{[1] Section 127 of the Finance Act 2008
[2] Paragraph 19(2)(b) of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007}