Talk to united as I believe you get one hour free at yotel. I fly into lhr on delta all the time and as a business elite customer / medallion we get use of a hotel room for one hour for free but if we come in just after a united flight the attendant says that we have to wait because they're in there and makes it seem like its a free benefit for them to.
Also best way to get into central london is kabbee.com It's for the Minicabs NOT the black cabs, I've been quote £125 from lhr to my house in NW london on a black cab or can take a minicab for £26- they are ligitimate, some of the time yes you get a shabby van, but sometimes you get a BMW or the like for the same price. And into central should be less time than to my house. You can't hail a minivan you have to prebook them.
Also just on a side note, ever since bmi went under star doesn't have any airline that calls lhr a hub, correct? So basically until hopefully virgin Atlantic joins star (I know, i know I can wish!) we can't use london as a stop over because no one calls it a hub, right? (which doesn't effect your plan)
On another side note if these flights into london go out the window OR if you get turned off by the stupid crazy high taxes lhr has, go through ZRH. I fly US/UK-South Africa frequently and prefer to fly via ZRH for their business class. Just an idea!
Enjoy your trip
Kyle