The closest equivalent UK airline is probably FlyBe, but SWA has more lenient refund policies and more generous bag allowances.
SWA is a dependable major airline with nearly full-service: the only traditional option they do not offer is interline accommodation for baggage on a connecting flight from another airline, or emergency accommodation on a different carrier in the event of mechanical failure. (Mechanical delays are very rare on SWA. They more often have issues with weather delays because they route a lot of their flights as milk runs that hopscotch across the US during the course of the day; that means that weather at any one of those stops can cause a ripple-delay effect. Note that SWA will not actually create itineraries that include more than 2 stops, and those are uncommon. If you really wanted to do several takeoffs and landings on the same aircraft all day long, you would have to go out of your way to book it that way on purpose.)