Tiger's conclusion I agree with, though here are some further points for you.
Though you use the term 'common land' it is unlikely to be as such. True Common Land appears on the register of commons held by the County (or Unitary Council). It is not owned by anyone and it is unlawful to drive onto true common land with a motor vehicle more than about 15 metres off the public carriageway (might be 10 metres - some small amount, anyway). Much land described as common land is not - it may be actually owned by a public body such as the National Trust.
Does that change the price of fish? - probably not. Unless you can identify the owner of the land in question (and if there is open land on the far side of this track, opposite your house, then the ownership of all the land is probably to the same person/organisation) and establish your right to pass/repass along it, it is doubtful that any of you actually have a legal right to put a vehicle on there.