I rent a room in a shared house, can bailiffs turn up?

Yes

The bailiff may take control of goods where the debtor usually lives or carries on a trade or business.^[1]

If the shared house is a licensed House of Multiple Occupancy (HMO),^[2][3] then the bailiff may not break entry into the room occupied by the debtor, unless the bailiff is recovering a court fine,^[4] or money owed to HMRC.^[5]

^{[1] Paragraph 14(6) of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007
[2] Section 1 of the Management of Houses in Multiple Occupation (England) Regulations 2006
[3] See Bailiffs and Houses of Multiple Occupancy
[4] Paragraph 18(b) of Schedule 12 of the Tribunals Courts and Enforcement Act 2007
[5] Section 127 of the Finance Act 2008}