Livestock transport is a regional trade, so this is a short starting list rather than a national directory.
Read the transporter authorisation rules: www.businesscompanion.info. Anyone transporting livestock for an economic activity needs a valid Transporter Authorisation, and longer journeys need a Certificate of Competence. Check before booking a haulier for the first time.
No paid placements. Run a UK business that fits here? Email hello@farmhq.ai with your business name, area covered and website.