Can bailiffs seize goods from self storage units?

Yes

But the bailiff must apply for that authority separately.^[1]

When bailiff are instructed to recover a debt by taking control of the debtors goods, they may only take control of those goods which are on premises where the debtor usually lives or carries on a trade or business.^[2]

The bailiff may also take control of the debtors goods found on a highway,^[3] anywhere in England and Wales.^[4]

If the bailiff wants to take control of the debtors kept anywhere else, including a storage unit, he must apply for that authority to the court.^[5]

The bailiff is probably unaware the debtor keeps goods in a self-storage unit unless he finds paperwork telling him about it.

^{[1] Paragraph 15 of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007
[2] Paragraph 14(6) of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007
[3] Paragraph 13(1)(b) of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007
[4] Paragraph 11(1)(a) of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007
[5] Civil Procedure Rule 84.9}