Funny that - I too used to live under the flightpath for LHR 27. I was on Seagrave road in Earls court. Where is your roof terrace?
When I was learning to fly and after talking to Lyneham and not understanding a thing they were saying to me I quickly bought an ICOM 22 something, the one with the VOR included. It cost me a bit but I never regretted the expense (used it in Africa in June after electrical problem in the AC). Get a transceiver and carry it in your flight bag. You never know!
I actually bought mine on a business trip in California (though it would be cheaper than at Transair in London. As it happens it was not!). Anyway. shortly after I bought it I found myself at Bakersfield airport, managed to get the tower frequency, turned the thing on...and the first call I heard was a mayday call from a guy who had an engine failure on finals (or final, whatever). He made it!
I am told that the many cheap receivers don't tend to last too long.
A roof terrace under LHR and your home airfield near Stanstead? Where do you fly from?