The Law of Allotments 5th Edition states:-
"Obviously any allotment tenant must have a proper means of access to his allotment, for himself and his necessary equipment. If the allotment adjoins a highway there will normally be an existing gate, but the making of a new entrance onto a highway will amount to development for the purposes of the Town and Country Planning Act 1990, and so need planning permission. The tenancy agreement should include, preferably expressly a right to use the existing paths between other plots so as to enable a tenant to reach his own allotment, and there should be a similar right across any intervening land belonging to some person other than the allotment landlord, between the allotment land and a convenient highway."
I think there would also possibly be some reference to right of access in Disability Rights law.