Free Traffic Legal Advice

Hello, I received a parking charge notice from parallel parking limited, I called on an industrial park in Coventry to make a purchase from one of the companies on the park . The industrieal site is only accessible by car it's on a duel carrage way with no pedestrian access, it was a bank holiday so most of the companies on the site we're closed the car park for the company I was visiting was was full, mainly with their own vehicles so I parked  on the road adjacent to the companies parking area .  The parking company  painted yellow lines on the road but it is private site I completed my purchase and left. if I had abided by their parking signs it would have meant that I was not able to stop at all and would have had to have left the site and returned in the hope of finding a parking space and done this until I could which is your is not viable it would have been roughly 3 mile trip onto the dual carriageway down to an island at one end back to an island at the other end and then back down halfway to the site I explain this to the company but they were not interested and I've since had a solicitors letter ,regards robert