Can bailiffs take goods without me signing a controlled goods agreement for council tax arrears?

Yes

Bailiffs have four methods of taking control of the debtors goods,^[1]

secure the goods on the premises where he finds them

secure them where he finds them on on a highway

remove them and secure them elsewhere

enter into a controlled goods agreement with the debtor

The bailiff may choose the method for taking control of the debtors goods.

The making of a controlled goods agreement is not compulsory, and in reality, it's rarely practiced because bailiffs earn more money by taking the goods, usually a vehicle and charging storage fees,^[2] (which must be reasonably and actually incurred).^[3]

When a bailiff makes a controlled goods agreement, it is usually because he does not want the debtors goods, or they have little sale value, or they have a high sentimental value to the debtor.

^{[1] Paragraph 13(1) of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007
[2] Regulation 8(2)(a) of the Taking Control of Goods (Fees) Regulations 2014
[3] See Challenging High Bailiffs fees Detailed Assessment CPR 84.16}