Bailiff turned up at my previous address. New homeowner told me, what do I do?

Nothing

If you give your new address, the bailiff will jump straight to enforcement without giving a statutory Notice of Enforcement.^[1]

Without knowing what kind of debt or its origin, the bailiff is looking to recover, you don't need to take any action until the bailiff has given you a statutory Notice of Enforcement.

If you get bailiffs at your current address when the debt or the enforcement power has your previous address on it, you may be able to apply to stop the enforcement power and overturn the debt or liability.^[2][3][4][5]

^{[1] Contrary to Paragraph 7.1 of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007
[2] Council Tax, See Ways to stop Council Tax Bailiffs
[3]Traffic Contravention Debts, See Ways to stop Parking and Traffic Debts Bailiffs
[4] Magistrates' Court Fines, See Ways to stop Magistrates Court Fines Bailiffs
[5] High Court writs and judgments, See Ways to stop High Court Enforcement Agents}