Maybe I'm overly cautious (or just prefer making transits as calm and relaxed as possible), but with 4 people having to make your way off the aircraft and through the UK border, depending on whether you're in Y vs J, lines at immigration, that in itself could take upwards of an hour before you're landside. So for the sake of argument, take the 11:10am arrival time, conservatively tack on 50 minutes to taxi, deplane, clear the UK border and you're looking at 12 noon... then figure roughly 20 minutes each way at best depending on what site you end up going to... so there goes at least 40 minutes from your window... leaving a touch over 3 hours of "time to kill" before your flight to the states departs.
If it were a solo traveler, ok it might be easier to manage but with 4 people total trying to keep everything perfectly on schedule, it's not a window I'd find to be a relaxing proposition.
Of course then you need to sort out are you the type who wants to be at the terminal 3 hours prior to departure time to go back through the routine of security, etc. or can you squeak it a bit shorter and not be stressed? (again cabin being flown and accompanying benefits ie. fast track security, how well you know LHR, etc. may have an impact on that decision)... so let's assume you want to be back at the terminal 2 hours prior to departure to clear security and get to the gate, you're now down to a little over an hour of actual "free time".
Don't get me wrong, when I have a connection at LHR with a few hours, I regularly do the whole clearing through the UK border and popping outside for some "fresh air" (nicotine based), but I don't personally go off property as I prefer to avoid the stress of unforeseen hiccups and delays like traffic, etc.