Even more interesting.
I suspect you are going to need proper legal help on this one, if you can afford it.
If you are going to go to a meeting with them, take a friend to keep notes and just LISTEN to what they say - don't offer anything. You are the one in the position with a legal document that says you own the land - so just stick to restating that - and ask them on what basis they believe there is a ROW across this land.
The definitive map and statement relates to footpaths, bridleways, restricted byways and BOATs. Here's some stuff on these - this taken from Hampshire, who seem to explain it rather well. It is part of the LA's job to maintain the Definitive Map and statement - usually the Council Council do this (or Unitary Authority where there isn't a County Council). This does not relate to Highways.
http://www3.hants.gov.uk/row/locating-row/defi nitive-map.htm
Your suits seem to be confirming that it isn't part of this, so by implication, they are admitting it isn't a public footpath, bridleway etc. over your land.
So the implication is they argue it is part of the public highway. It isn't adopted - they admit that (an adopted road is one maintained at public expense). You therefore need to ask them on what basis they believe the land is part of the public highway, reasserting that you hold the land title to the land in question.
Then report back.