Can Bailiffs enter my children's room and take stuff like his PS4, TV, Lego sets etc?

No

Bailiffs may only take control of goods that belong to the debtor.^[1]

If the debtor is under the age of 16, the bailiff may not take control of the goods of the debtor.^[2]

^{[1] Paragraph 10 of Schedule 12 of the Tribunals Courts and Enforcement Act 2007.
[2] Regulation 10 of the Taking Control of Goods Regulations 2013}