Can bailiffs take my child's games console?

No

Bailiffs may not take control of goods of any debtor who is under 16.^[1][2]

Bailiffs should not remove anything clearly identifiable as an item belonging to, or for the exclusive use of a child (person under the age of 16).^[3]

Bailiffs must withdraw without making enquiries if the only people present are children who appear to be under the age of 12.^[4]

If bailiffs take control of goods that do not belong to the debtor named on the warrant, or enforcement power, the owner may make a third party claim.^[5][6]

In reality, bailiffs have no interest in taking video games consoles because they have little material value on the 2nd hand market. Bailiffs may target games consoles because those items are close to the debtor and the threat of taking it might trump up the money.

^{[1] Regulation 2 of the Taking Control of Goods Regulations 2013
[2] Regulation 10(1)(a) of the Taking Control of Goods Regulations 2013
[3] Paragraph 63 of the Taking Control of Goods: National Standards 2014, April 2014
[4] Paragraph 73 of the Taking Control of Goods: National Standards 2014, April 2014
[5] Civil Procedure Rule 85.4
[6] See Making a third party claim to controlled goods}