A refusal is not the end. Most are one line and prove nothing.
Check your flightAirlines refuse claims as a matter of routine, because a large share of passengers stop at the first no. The email is usually one line, sent from a noreply address, and cites "extraordinary circumstances" or "operational reasons" without saying what actually happened.
That is not a legal position. It is a filter. Under Article 5(3) the airline has to prove the cause was extraordinary and that it could not have been avoided even with all reasonable measures taken. You do not have to prove anything.
A vague one. "Operational reasons", "circumstances outside our control", "a third party supplier". These name no cause and prove nothing. Write back and ask for the specific cause and the evidence for it.
A specific one you can check. If they say a named storm closed the airport, or an air traffic control strike was running that day, that may well be genuine. Weather, ATC, airport strikes and bird strikes are real defences.
A specific one that does not work. If they tell you the aircraft had a technical fault, the crew ran out of hours, a crew member did not turn up, or the inbound aircraft was late, they have just told you why they owe you money. Courts have ruled on all four.
Reply in writing and ask for three things: the specific cause of the disruption, documentary evidence of it, and an explanation of what reasonable measures they took to avoid it.
Cite the case law by name. In Wallentin-Hermann (C-549/07) the Court of Justice held that technical problems inherent in running an airline are not extraordinary circumstances. In Krüsemann (C-195/17) it held the same of strikes by the airline's own staff.
A meaningful share of refusals quietly become payments at this point, because the person handling it can see you are not going to go away and that the file will not survive a regulator looking at it. There is a ready-made letter for exactly this.
If they hold out, take it to the national enforcement body in the country you departed from. This is the part people get wrong: it is the departure country that decides, not where the airline is based. A British Airways flight out of Lisbon goes to the Portuguese regulator, not the CAA.
It costs nothing and airlines take those letters considerably more seriously than they take yours.
Small claims exists and works. In England and Wales that is Money Claim Online, in Scotland the simple procedure. The sums involved are within small claims limits everywhere in Europe, you do not need a solicitor, and airlines frequently settle once proceedings are actually issued rather than defend a case they are likely to lose.
You have longer than you think to get there. The UK allows 6 years, France and Spain 5, Germany 3, Italy and the Netherlands 2.
Check what you are owed