I flew JFK-LHR-CDG a few weeks ago with an intentional long connection in London (~8 hours) to allow me to leave the airport and run some errands that needed to be done in person. My JFK-LHR flight ended up getting delayed by ~6 hours meaning that I wasn't able to leave LHR before my onward flight to CDG (which was the last available flight of the day). I'm now going to need to do a separate trip to LHR (and deal with not being able to go back to CDG after...) and was considering putting in a claim for delay compensation.
I'm assuming this won't be successful, since the delay was on the first segment and my arrival at the final destination (CDG) was on time, even though my reason for routing via LHR was to have those hours in LHR to go landslide.