Can a Bailiff demand their fees when the council withdraws the account from them?

No

Bailiffs cannot recover any fees and charges from the debtor when the creditor has stopped the enforcement.^[1]

Any fee dispute becomes a contractual matter between the bailiff and the creditor.

If the debtor applies for a stay of execution after the enforcement agent has taken control of the debtor's goods, any fees and disbursements paid by the enforcement made be decided by the court.^[2]

Any fee dispute can be resolved by the debtor applying for detailed assessment hearing.^[3][4]

^{[1] Regulation 3 of the Taking Control of Goods (Fees) Regulations 2014
[2] Civil Procedure Rule 83(7)(15)
[3] Regulation 16 of the Taking Control of Goods (Fees) Regulations 2014
[4] Civil Procedure Rule 84.16}