If it is a private road then no "fine" is permissible. You can only be fined by the police or a traffic regulation order. It is possible to impose a monetary penalty in a limited number of circumstances when there has been a breach of contract, but these are normally imposed by signage and if the signage is as you outline it would not be sufficient. Please send me a copy of any correspondence you receive and I will assist you in dealing with the case. There is no charge for this service.