Ignoring construction, which is a one off hit, improvements which ease traffic flow could be argued to be green, having vehicles stationary or close to it because of congestion is the worst possible scenario, and creating shorter routes (lower Thames Crossing) also has benefits. Given current fuel prices I cannot see there being a big increase in discretionary journeys from these improvements.
In areas with a widespread public transport system (London, and to a lessar extent Manchester, Liverpool, Birmingham and maybe a few others) not running a car is a possibility, however for vast areas of the country not having a car whilst survivable if you have no choice isn't something the majority of people in these areas would decide to do. Public transports lack of integration, unreliability, no early and late services and costs, particularly for say a family with 2 children means that a car is almost essential.
Building more roads only ever created more traffic, now whilst it does ease congestion at that point, it almost certainly makes congestion worst elsewhere.
Where did I say that people would not use cars at all?
I said that there could start to be a nice away from cars.
As a family with kids which lives in a rural settlement (population of about 9,000) we have just one car and try and user it as little as possible. Could we do without it, almost certainly not. Would it be useful if we had two cars, yes, however the cost of doing so wouldn't be good value (never has been).
The point being that these current high prices may just trip the balance for a few now people to consider using their car a little less and/or reducing the number of cars in their household.