You have 5 or 6 years to claim in the UK, so not too late to do so, but as you were not delayed arriving at your final destination you may find a claim refused on these grounds. It's an unusual case as we more often hear about the first flight being on time and the ex Middle East flight being delayed and QR (EK,EY etc) refusing claims, as they refuse to count the onward flight as part of the journey to the final destination. As such, I don't know if you have a leg to stand on.

Ignore the advice about approaching the CAA as it's not a requirement and they are toothless, although it might strengthen your case ever so slightly if they rule in your favour but you still end up in court.