Thank you Jimbob. Can I tackle your idea of permanent as opposed to temporary barriers?
I live in a county largely given over to stock rearing. The animals are rotated between fields to protect the grazing so much of the time they are empty. To protect the general public by fencing all the PROWs that cross fields where stock might be grazed would be a major undertaking as well as expensive, as would the maintenance of the fencing. Moreover, when the the stock graze the fields they include the line of the PROWs. Once stock are kept permanently clear of the paths, another means would be need to be found to keep the paths to stop them being choked by seasonal growth.
IMHO lines of parallel barbed wire one meter apart either side of every PROW that crosses grazing land would be a complete eyesore and would turn the countryside into little more than a theme park. Such a proposal could also be detrimental to the current PROW network. If landowners are forced to fence off paths, it will give them an excuse to challenge the continued existence of the PROW network, especially those sections that are little used.
I can understand that some people do not want to walk in fields with livestock in them and they are at liberty not to. However, farms are first and foremost businesses, not recreational facilities - that is a bonus for us and rural communities but brings very little return to the farmers themselves. This proposal would only serve to aggravate the the relationship between the farming and the walking communities.