In reply to kipper12:
1. check the council's definitive map of PROWs. If it's on there as a BOAT, anyone can drive along it.
2. If it's not on the definitive map, ask the council if it's on the List Of Streets. If it's on there, it's a public road (even if it doesn't look like one) and anyone can drive along it.
3. If it's not on the DM as a BOAT or on the LoS, do the kennels own their land and property? If so, ask them to check their deeds to see if they specify a private right of vehicular access along it. If they only rent their premises, check the lease to see what that says about rights of access.
4. If none of these steps gives you your answer, it starts to get difficult and/or expensive and you probably need a solicitor, unless you're happy to just ignore the farmer and carry on as you were. Happy to advise further if steps 1 to 3 give you no joy (this kind of issue has been a big part of my working life for 25 years).