The Wales Coast Path[0] links up with it, so (aside from the small gap in Cumbria), you can walk all the way round if you start and end at the Scottish border.
There’s also the Hadrian’s Wall Path[1] that allows you to link back into a loop new the Scottish border, though it misses out a section of the English coast in the North East.
[0] https://en.wikipedia.org/wiki/Wales_Coast_Path [1] https://en.wikipedia.org/wiki/Hadrian%27s_Wall_Path
A section? All of Northumberland, as Wallsend is in Tyne and Wear.
The task of walking (or measuring) the whole of England's coastline is made a bit more difficult by the existence of various islands classed as part of England.
e.g. Isle of Wight, St. Mary's Island, Coquet Island, Lindisfarne, the other Farne islands, etc.
Similar to Hadrian's Wall, there's the Offa's Dyke Path which roughly follows the Welsh border all the way up.