Mini cabs are the cheapest taxi service in London.
Find online or call this one: “Monarch radio cars” tel:02089947777
Let them know your flight number and the arrival time plus time for customs and luggage (about 30 minutes). They will wait for you outside. The price would be about £20 for 4 seats car to get from Heathrow to Kensington. The Professors would have to pay extra :wink-wink£20:wink-wink if coming from Gatwick. The only problem is if your flight is delayed.