Qatar will be the only carrier flying direct from the Southwest of England / Wales to the gulf they will very likely do disproportionately well in relation to the aforementioned, both of which have extensive competition from the likes of Emirates, Etihad and Turkish.
What you mean is that will be the only carrier flying direct to DOH, i.e. if one wants to travel to AUH, DXB, BAH etc. etc. etc. they they shall need connecting flights, as they would to travel onwards to Asia etc., but then BRS has been offering connecting flights to such destinations for years with the likes of KLM and Lufty with several flights daily so I can't really see the people of the south-west trudging across the Severn for one flight every couple of days when they have alternatives from their side of the Severn, possible but I can't see it.
Meanwhile CWL has had KLM for a few decades now offering connecting services to M. East, Asia etc. so all that Qatar are actually bringing to the table are direct services to DOH and an alternative to other long-haul connections that have been in place for decades.
But ... Whenever I was travelling to Asia I couldn't achieve a good connection combined with a competitive fare with Qatar, either I needed to pay thru the nose for a short connection or I needed to layover in DOH for perhaps 20 hours and with only a few services per week to/from CWL I can't see that Qatar are going to be able to offer very many travellers short connections and/or competitive fares.