Can bailiffs take a vehicle used to take livestock to a vet?

Yes

Unless the vehicle's value is under £1,350.^[1]

If the vehicle is under £1,350, the debtor may make an application to exempt goods.^[2][3]

If the debtor is a company, the exemption only apply to to goods used by the debtor personally.^[1]

If the vehicle is owned by a farm, and the debtor is a person, the bailiff may not take control of the vehicle.^[4] The owner can make a third-party claim to controlled goods.^[5]

If the debtor is a farmer, the creditor must provide the court, if requested by the court or the bailiff, an official certificate, dated not more than three days beforehand, of the result of a search at the Land Registry as to the existence of any charge registered against the debtor under the Agricultural Credits Act 1928.^[6]

If the creditor fails to provide the official certificate within 7 days of receipt of the request, the court, of its own motion, or on the application of the bailiff, may order the creditor to provide the certificate.^[7]

^{[1] Regulation 4(1)(a) of the Taking Control of Goods Regulations 2013
[2] Civil Procedure Rule 85.8
[3] See Making a claim to exempt goods
[4] Paragraph 10 of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007
[5] See Making a third-party claim to controlled goods
[6] Section 5 of the Agricultural Credits Act 1928
[7] Civil Procedure Rule 83.21}