Further precision might be possible by actually splitting counties, but the rule of thumb is that "bath" is northern and "bahth" is southern. Things are further complicated by the fact that those in the south-west don't say "bahth", but rather "baath", and don't really have proper southern accents. So maybe the proper divide is south-east versus everywhere else (might as well call it north-west). So looking at the map again, the borderline counties inside the south-east would be Hampshire, Berkshire, Oxfordshire, Northamptonshire, Cambridgeshire, Norfolk. So, yes, Cornwall is in the north-west. Deal with it.
But then if someone put a gun to my head and said I had to come up with a north-south divide that went straight across, that would be rather tricky. It would have to be a compromise. I don't think I'd be sacrificing too much by saying anything north of Bury St Edmunds is northern, and Bury St Edmunds and south is southern.
Edit - on the Wikipedia page, that map has the county names on.
![Image](https://upload.wikimedia.org/wikipedia/commons/thumb/1/14/English_ceremonial_counties_1998.svg/1030px-English_ceremonial_counties_1998.svg.png)