Any source for your £600bn claim? A report from the Greater London Authority written in Feb 2016 gives a figure of £364bn: https://www.london.gov.uk/sites/default/files/gla_the_london_economy_report_full_low_res.pdf which is around 25% higher than the North of England:
https://www.ft.com/content/d4bcaaba-dbbe-11e5-98fd-06d75973fe09
You could argue up here many of the cross-Pennine road routes aren't accessible 365 days a year meaning cross-Pennine rail routes are imperative to the North's economy.
Actually there was a dollar-pound coversion error there so the figure that I should have stated was £483million. That was calculated from:
the ONS figure for London's GDP is 22% of the UK figure:
see references10 (and also11) on this page:
https://en.m.wikipedia.org/wiki/Economy_of_London
The UK GDP for 2016 was £2.757 trillion from the World Economic Outlook Databse, referfence 1 on this page:
https://en.m.wikipedia.org/wiki/Economy_of_the_United_Kingdom
see references10 (and also11) on this page:
https://en.m.wikipedia.org/wiki/Economy_of_London
The UK GDP for 2016 was £2.757 trillion from the World Economic Outlook Databse, referfence 1 on this page:
https://en.m.wikipedia.org/wiki/Economy_of_the_United_Kingdom
My main point though is that despite London being a world-class city, and in many markets, a world leader, it's road infrastructure certainly isn't. In order for the city to function at a level that makes such a large contribution to the UK economy, the workforce cannot rely on private transport commuting as the city would quickly grind to a halt.
Therefore, an integrated transport system is provided at reasonable cost to encourage that workforce not to fill the roads with one person per car. There are both carrots and sticks here, - good public buses and train services and ever increasing congestion charges and parking restrictions for private motorists.