In reply to mnyateley:
I really would try and park on the outskirts and then cycle the last bit. I've been known to get the train to Waterloo with bike and cycle from there. Do check what the current restrictions are on bikes, though.
> I don't think my wife would want to cycle very far in the traffic to reach the closed roads of the route.
It's really not that bad if you use the bus and bike lanes and spend a bit of time route planning.