To start with bednobs is right that the solicitor should be dealing with it.
It looks like either the solicitor has fouled up or (as Tony says) the seller had an obligation to disclose any difficulties they had in terms of disputes with neighbours (there is a standard enquiries question that purchaser's solicitor asks the seller's solicitor about disputes).
Next, the owner of the land has every right to park on his land, HOWEVER if there is an easement in place then the neighbour is obliged to enable the terms of the easement to be met. This is unfortunately where things can get fouled up because if the easement just says a right of access by motor vehicle and nothing more then there is no clear definition about the width of the access that is required. The solicitor should have picked up on this, even if the sellers incoreectly failed to acknowledge a previous problem.
Force the issue with the solicitor, if no joy, complain in writing to the head of practice.