Speaking as someone who enjoys an invigorating sea swim, whilst there are some folk in wetsuits swimming in southern waters, I can't say I've ever noticed they're in the majority. I've swum off approximately 70 beaches in Dorset, Devon and Cornwall (both coasts in the latter two cases) and can't say I've noticed a theme.
The sea temperature of the Irish Sea actually surpassed the south coast in summer 2018. I swam at Morecambe in August 2018 (carefully waiting till the tide was in) and it was noticeably warmer than in Devon and Cornwall. The Atlantic and Channel tend to vary less in temperature year round than the more enclosed seas do - in warmer summers, the north-west can easily have warmer seas than the south-west, although the winter seas will invariably be colder. The eastern end of the Channel is warmer than the western end in my experience, but the North Sea is noticeably colder than the Irish Sea.
Back on topic, the official government definition of the north is Cheshire, Merseyside, Greater Manchester, Lancashire, Cumbria, North Lincolnshire (area around Scunthorpe and Grimsby), Yorkshire, Durham, Tyne and Wear and Northumberland. I'd agree with that. Grimsby is further north than Sheffield and I can't see how it can be considered part of the Midlands. Geographically Cheshire is more Midlands, but far more linked culturally to Liverpool and Manchester IMHO.
I've always thought you could argue that geographically Liverpool, Manchester and Sheffield are all north Midlands rather than northern - far closer to Birmingham than the Scottish border. Culturally however they're certainly not. That said, Bristol is about the same distance from Lands' End as it is from Yorkshire and no-one considers that Midland (except maybe Penzancers).
I've always found it odd that Norfolk often seems get lumped in with the south when geographically it certainly isn't. I've always assumed this is because it's got average transport connections to London and pretty uninspiring connections to anywhere else.