Nope, no park and ride in London.
It's called the tube
and don't drive into London, it's a foolish thing to do.
One of the popular shots (Raymond has done it but I can't find an example now), would be the shot of the couple on the millennium bridge with St. Paul's in the background.
Also, if you get off at London Bridge (not that far from the millennium bridge), and head to the tooley street exit, if you go right from there you can walk down to moor London.
From there, you can quite easily shoot The Shard, Tower Bridge, The Tower of London, Hms Belfast, The mayors building, and the Walkie Talkie building in the background. (All at different angles) so that's an option.
You could also get off of Canary Wharf and there's quite a few places out there. It wouldn't be my first choice mind you... Whilst there's plenty of skyscrapers there, I'm not sure you'd be able to actually get the couple far enough back, to get everything in, but it'll probably be less touristy.
Both Canary Wharf and London Bridge Stations are on the Jubilee line. St Paul's I can't quite remember what line it's on.
As for coming in from Oxfordshire, finding a national rail train that goes in to one of the underground stations with an overground would probably be a better option. Normally this would be kings cross, Liverpool street, Paddington or London bridge, but could be one of many, don't know about that direction. There might be a tube line out there mind. A quick google should answer.
The final things I'd say regardless of location is make sure you have a tube map, and know how to get from your tube station to location. The tube system is one of the greatest ways on the planet to get around the city. Also, have backup options to get from one tube station to the next, and check which lines have delays.
kd