I live nearby Frankfurt airport and every few months or so the DFS (German ATC) issues a press release about inspections flights.
Sample from their homepage:
Flugvermessung am Flughafen Frankfurt (Flight inspection at Frankfurt Airport)
Noise disturbance to be expected during the day and at night
14.11.2016.- In the period from 17 to 20 November 2016, calibration flights will be conducted at Frankfurt Airport.
The accuracy of the instrument landing systems of the southern runway and the centre runway will be inspected for landing direction 25 (westerly weather patterns) of the southern runway and 07 (easterly weather patterns) of the centre runway. The calibration aircraft being used is a twin-turboprop Beechcraft Super King Air 350. During this time, noise disturbance is to be expected during daytime and nighttime hours.
Despite the night curfew at Frankfurt Airport, technical flight checks such as calibration flights may also be conducted at night as they would have a great impact on regular air traffic during the day.
The calibration of technical facilities is indispensable for the safety of air traffic. DFS would like to apologise for any inconvenience caused by such flights.
This one was for RWYs 25L and 07C but three months earlier they did similar flights for RWY northwest (07L/25R).
It's interesting (and attracting) that flightradar24 shows the flight around LHR from your question.
Next time I hear about inspection flights in my area I'll have a look at flightradar24 too.
Update: A few days ago DFS announced further calibration flights from 16 to 19 February 2017 around FRA/EDDF to inspect ILS accuracy for RWY northwest (07L/25R). I figured out they use (at least) two aircraft, D-CFMB and D-CFMD. This time it was the latter. They flew on Feb 16 (left) and Feb 17 (right):
But the funniest one must have been on Feb 15 from DRS (Dresden) to Berlin (SXF), rendering kinda crop circles:
All pictures from FR24.