No. According to the Heathrow Airspace and Future Operations Consultation hundreds of planes will fly at low altitude over Richmond Park – a national nature reserve – for the first time. I can’t link to the Guardian article as you need to have posted 10 times to be able to include a URL. Here’s a quote however, "It seems irrational then that the government is allowing Heathrow, as part of its plans for the third runway, to propose routing for the first time 47 low-flying arrivals as well as between 17 and 47 extra departures every hour directly over Richmond Park, London’s largest open space, a national nature reserve and a site of special scientific interest.”
And another "Under the Heathrow expansion plans, hundreds of planes would produce noise levels of up to 80dB – nearly eight times the WHO guidelines – flying at 1,500 feet over the park."