You could probably try with ADS-B exchange. You can query their server using the following url https://public-api.adsbexchange.com/VirtualRadar/AircraftList.json
It will give you a list (in the form of a json string) of all the aircraft currently being tracked (the "acList" tag contains the list of aircraft). Most aircraft operating in major airports are equipped with ADS-B transponder so they would appear in your feed.
You can of course filter the json string around your area of interest. By reading the documentation, it looks like appending ?fAir=LHR would give all the aircraft currently tracked that departed from/en route to Heathrow.
It should be pretty easy to then parse the string to get the information you want (carrier, type of aircraft etc.). All programming languages these days have libraries allowing to easily and quickly parse json. I am not sure how often the server refreshes it's data...every second maybe?
Not the most practical solution, as I am not sure if there is an easy solution to work out ETA or departure time but you could give it a try (it's free!)