I only go to London on business travel so price isn't as big of a deal but I take the Heathrow Express for time purposes. In morning traffic after the red eye from NYC it's much faster than either a cab or the tube.
OT but check the flights from NYC to City Airport they are much better than anything you can get from/to Heathrow unless you are flying with mile high club ;)
The only flights I'm aware of that fly NYC-LCY are the BA flights that are all business. The nice thing is that you get to pre-clear immigration in Shannon, Ireland but unfortunately I'm not quite important enough to demand $10k flights.