Can bailiffs remove a fireplace or wood burning stove?

No

Exempt goods of the debtor include sufficient lamps or stoves, or other appliance designed to provide lighting or heating facilities, to satisfy the basic heating and lighting needs of the debtor’s household.^[1]

Bailiffs cannot take a wood-burning stove, or any cooking equipment required to satisfy the basic domestic needs of the debtor and every member of the debtor’s household, including (but not restricted to) a cooker or microwave.^[2]

If a bailiff takes control of exempt goods, the debtor may make a claim to exempt goods.^[3][4]

^{[1] Regulation 4(1)(b)(viii) of the Taking Control of Goods Regulations 2013
[2] Regulation 4(1)(b)(i) of the Taking Control of Goods Regulations 2013
[3] Civil Procedure Rule 85.8
[4] See Making a claim to exempt goods}