Where can I find a list of past flights at LHR?
If you're lucky, you might just get it for free (see halfway down this page):


  We have provided a data drop of historical flight information for
  specific airports or airlines, on a one-off basis.


As for the runway data, it's harder, since I don't know of any website which records it. You can have a look on Flightradar24 for which runway is in use at the moment depending on the aircraft positions, but apart from that it's probably not going to be easy. You might want to email the airport directly and ask if they could provide a figure for that month for each runway, but I'll doubt that a single source has the details for each and every flight.

If you get to it, have fun sorting out 40,000 flights ;)