This is a very small road, a vehicle would struggle to get down. Large rocks are often placed across to prevent vehicular access. As of a few days ago this was not the case.
It is currently a right of way on the definitive map (https://maps.durham.gov.uk/OLBasic2/Index.aspx?appid=66).
It is not a council adopted highway (https://maps.durham.gov.uk/OLBasic2/Index.aspx?appid=61) nor is it council owned (https://maps.durham.gov.uk/OLBasic/Index.aspx?appid=59).

I would say it is not advised to try and travel on this road to gain access to the A19, as it is :
* Assumed private property
* Often blocked with large rocks, making vehicular access impossible
* No slip roads at all onto A19.