You are struggling a little bit here to understand how the world works. Let me try to make it more clear. The general public will not stand for higher taxes and less road development. However we look at it, the car is a deity around the world and people will not give them up, no matter how fast one can get to the middle of town. Let's look at it another way. There are many cheaper alternatives to underground systems - light rail being the most obvious. The people of this country would certainly not pay higher taxes for a scheme when there is a cheaper alternative. I live in Leeds. I'm certain an underground system in Leeds would be an advantage, but not over light rail. I though, like most people in this great city, would not pay higher taxes for either of these schemes. Your plan also falls short on the motorway lanes issue. A motorway is designed to move traffic quickly between points over large distances. An underground network is designed to move large amounts of people around a small, densely populated area. So, if you are missing my point, an urban transport network would not reduce the need for people to use a motorway - hence, extra lanes would still be needed. If you have a rock solid plan with a water tight business case than can potentially be implemented without inconveniencing the public financially, please, by all means, take your case to the government. If your plan really is what you have pointed out here, you are just wasting your time.
Maybe I don't understand how the world works, but nevertheless I have a few comments here:
1. I wasn't suggesting that people give their cars up - not sure where you got that from!
2. I disagree that an underground network is JUST designed to move large amounts of people around a small, densely populated area. Take the London Underground. There are multiple connections points to National Rail (Paddington, Euston, Kings Cross, etc.), a connection to the Continent (Eurostar from Waterloo/St Pancras) and a connection to Heathrow airport.
3. From 2, it follows that as underground networks serve to connect people quickly (ie avoiding road traffic) to main National routes, that the absence of these networks can discourage people traveling on the main routes - they may be alright at the London end of the journey, but the network at the other end of the journey may well not be upto the same standard, making the car more attractive when the journey is considered end-to-end. So, I disagree that more underground networks wouldn't take any traffic off motorways.
4. Light rail is a possibility, granted. The initial cost of construction would be certainly be less than that of an underground system. Imagine, though, if the London Underground system didn't exist, and there was light rail instead. The light rail would be competing for road space with other traffic, e.g. cars, taxis, buses. So there would be even more congestion overall in London, and what does congestion cost? money! How much? lots! Perhaps the optimal solution would be a mixture of rail and light rail.
5. The world is a-changing! There are issues concerning global warming, and the fact that fossils fuels may become scarce in a couple of generations that we can't ignore - if we wait to act until we are forced to by circumstances, the solution will likely be less good (maybe back to the horse and cart!?) - you can't build an extensive railway system overnight.
6. As fossil fuels become increasingly scarce, fuel such as petrol will become a lot more expensive, making alternative systems such as rail/light rail relatively more attractive. As it is not hard to predict that fossil fuels will become more scarce, we can anticipate that eventuality by investing in extensive rail systems.