Can you take non UK airlines outside of CAA or any other regulatory body to small claims court?

RKClarke

Specifically in my case, Qatar Airways. 
Details summary - Flight from Maldives to Doha (for a connecting flight to London) did not take off due to technical difficulties (Boeing 777) , we sat on plane for c4 hours as they tried to fix it. They failed, we were disembarked, put up in hotel, came home on Airbus A350 24 hrs later. Number of claims: 1) we'd paid for seat upgrades, in a 2 seat config, not honoured A350 was 3 seat config. 2) Before flight issues we received email changing flight planes, took 3 calls @50 each to resolve when still in Maldives. 3) paid extra days parking.
Qatar Airways response - received months after claim raised, stated they are permitted to change our seats (of course) and those supplied were similar (they weren't, narrower, 3 abreast, the sort you wouldn't pay upgrade for).. As regards the flight delay, Qatar said it was due to circumstances outside its control. It was their plane with a technical issue, not the weather, strikes, atc delay etc. 
I responded stating these differences of opinion but simply got a version of the same original response.
I tried CAA, they do not cover Qatar Airways, nor the other one CAA redirects you too. I thought of small claims court approach but not sure that's possible for a foreign registered company.?