The titles are West Midlands and West Yorkshire, neither have "greater', and while the former is arguably a functional city area, the second is not.
This is a relevant point to make, because you seem to be getting confused between physical size (volume) and contribution (profit). It is highly debatable whether London does in fact make a profit, or whether if you strip away "the City" and the money shuffling whether it's actually a black hole.
Meanwhile, Greater Cambridge with its mere population of under 300,000 is one of the most profitable areas in the UK, and Leeds - in West Yorkshire - population just 780,000, enjoys one of the highest sets of earnings in the north.
It may be clear that at the moment demand is greatest in London, but that neither contains the evidence you think it does nor does it mean that state of affairs should carry on forevermore.
Your view of London's history vs elsewhere is somewhat rose tinted. Prior to the mid-eighties, London was in a very sorry state, and it continued to lose population every year from 1951 to the mid to late nineties. Your portrayal is of a place that naturally "won". While being the seat of government always helps, in fact its turnaround is simply the effect of urban design, policy and investment.
When Liverpool, Newcastle and Glasgow are individually bigger than some (wealthy) capital cities, and each lies in its own coastal region rich in varied natural resources useful in the modern age, the notion that modest investment of £10bn each couldn't rapidly double or even triple their net contributions just isn't credible, especially when we know the contributions are currently half of what they should be.
