If the Plat reservation agents can't help, then I would suggest picking a few Marriott's that you would like to spend the day at and call them directly. The local staff should be able to tell you if they have day rates, what those rates would be and help you make a reservation.

Though I would ask why you want a day room at all? Given that you don't have a lot of time in London, by the time you get through customs, get to the Tube, get into London and then return, you don't have a lot of time to be sitting in a hotel room. If you are looking for a place to shower and freshen up a bit, I think there is an arrivals lounge in LHR that you can buy a day pass into (and it may be cheaper than one of the hotels.) But if you really want a hotel, unless there is a specific reason for a downtown one, I would then suggest looking at the LHR Ren or Marriott as they are right there at the airport and tend to have some of the least expensive rates around the London area.