There is a gate in the fence, but there is no gap in the central reserver. You have to climb over it.
If you look on the Stockton Council definitive map here: you can see the right of way. https://imaps.stockton.gov.uk/?navigation=true&gazetteer=true&infopopup=true&layerswitcher=true&layerswitcherLegend=none&layerswitcherOpen=false&fullscreen=true&panelTitle=Stockton+Land+Ownership&panelDesc=&profile=mapsources%2FWebTeam&layers=Adopted_Highway%21vis1%2CCouncil_Ownership%21vis1&easting=444404.65&northing=519032.72&resolution=1.0000005399999998&srs=EPSG%3A27700&basemap=mapsources%2Fbase_ospremium

It seems when the road was built the right of way/path remained, but no designated crossing point was included.

Thanks Jez. I've worked out the squaring now, but will need to read up a bit more about the court yards. Thanks for the help.