Lime Tree Apartments is on the Piccadilly line of the London Transport Underground network – although on this line, the trains run overground from Baron’s Court through to Heathrow Airport.
Journey time from Northfields to Heathrow is approximately 20 minutes by Tube and similar by car. Into the centre of London, allow approximately 30 minutes by tube and similar by car.
There are lots of plans to modernise the London Underground. Here is a clip, with Tube train destination showing “Northfields” !