https://www.nfuonline.com/ps12070-briefing-mud-on-the-road
To make a successful claim against the farmer (or contractor, as appropriate) you'd need to show that he'd been negligent by either not cleaning mud off his vehicle (where it was possible to do so) before allowing it onto the road or through not cleaning the road as soon as was practical to do so after the mud was deposited.
However if the farmer could show that
(a) he'd cleaned as much mud as possible from his vehicle before taking it onto the road ; and
(b) that he couldn't reasonably have had time to clean the road (because, for example he'd only driven along it a minute or two before you did) ;
then a court might take the view that he'd not been negligent.