That's English beurocracy in a nut shell! no matter what you wish to achieve you have to go around in at least three circles first!
I was under the impression you would need a passport even to fly internally as when i looked into flying north a good few years ago from Heathrow i still needed a passport!
is there no other travel options available for you to get to London?
one tip, buy an oyster card, it will reduce your travel costs whilst you are here unless you have a free travel pass that is recognised here.
if you decide to drive there is a daily congestion charge to pay and parking is a nightmare in some places but if you are disabled you can register for free charging so the you do not have to pay the congestion charge.