The real reason London is rich at all is because it was a trading depot with the continent. It made money from goods leaving England, and entering England. Later on, like Paris, it became wealthy off running an overseas empire, and when that empire vanished it turned to nearer territories.

London has centuries worth of investment from everywhere else based on that. That money has stayed there, and money is spent constantly on infrastructure which helps it make more money. Contrast this with Liverpool, Cardiff or Belfast which suffered decades of decline for various reasons and a fraction of the investment.

If the capital had been moved to Liverpool back at some point in the Middle Ages, then that would have remained a wealthy city instead of becoming a basket case in the eighties. The presence of the civil service and government alone would have kept Merseyside wealthy, and would have made it a huge tourist centre. Bigger than now, and even that was mostly to do with the Beatles.

By the way, the state funded Wembley refit cost more than the construction of the Scottish Parliament. Guess which one got all the negative press?