Any article which seeks to explore the problems of northern England and doesn't mention the weather is fundamentally incomplete.
I've lived in every part of England, but being in the north west for the last decade has highlighted how much our mental health can be damaged by constant grey skies and rain. A population predisposed to feeling hopeless naturally leads to a less vibrant economy.
The diagram of the northern "urban" centre also fails to point out the Peak District, though you can detect it by noticing what looks like an obvious gap in the middle of the circle. In the middle of the London circle is, of course, the centre of London, world-famous capital city of the United Kingdom, seat of power of its government and monarchy. In the middle of the Northern circle? Some mountains and the occasional picturesque little village...
(The weather might also be a factor here too. The elevated regions are much colder, snowier and windier, causing problems with transport. Getting between Sheffield and Manchester at this time of year can be a painful business.)
In my comparisons with the Netherlands I explore this in detail. The centre of the Netherlands' main urban region is a six metre below sea level swamp that the Dutch never have and never will build on and which is just as much of an obstacle to agglomeration as the Pennines. So I really don't think this matters.
As for the weather, Ireland, Scotland, Belgium, The Netherlands, and Denmark are hardly renowned for their fantastic weather and they're all doing much better than North England. Meanwhile Southern Spain, Southern Italy, and Greece are lovely places but not doing well economically. I don't think the weather is a good excuse for Northern underperformance.
The bad weather places you mention have largely uniform bad weather, which is not true of England - the south east is noticeably warmer and drier than the north west.
Weather is of course only a contributing factor, just like the historical influences.
I've lived in every part of England, but being in the north west for the last decade has highlighted how much our mental health can be damaged by constant grey skies and rain. A population predisposed to feeling hopeless naturally leads to a less vibrant economy.