Yes, London is planning to close Oxford street, it just has to figure out how buses can be redirected in a smart way to allow shoppers to get there easily. Furthermore, one of the busiest intersections (bank) will be closed to all vehicles but buses from next year on. The fact that it will even be closed to black cabs is a strong signal.
In addition to that there are also plans to revert some of the 70's car-friendly areas in the city. Mainly roads that were designed to be one-way to ease traffic flow will be made less car-friendly. This is supposed to slow down traffic which should make it safer for cyclists and pedestrians. ("The one-way system encourages high traffic speeds, which is at odds with the City's aspiration for safer streets within the Square Mile.") [0]
I'm not aware that there is any project in London at the moment that will ease congestion, it's all about making life for pedestrians and cyclists easier. As a cyclist, I really welcome that trend. The new cycle-superhighways [1] are a great thing, IMO.
[0] Project 48: https://tfl.gov.uk/travel-information/improvements-and-proje...
[1] https://tfl.gov.uk/modes/cycling/routes-and-maps/cycle-super...