@Susan ***
It certainly is not only 2 airlines asking for visa or onward ticket.
I already experienced it for other airlines, and that is OK.
All airlines should do it, but most only do incidentally to save time.
The British passport, your skin color and the class you fly have nothing to do with these requirements. You choose not to buy a visa, that means you decide to use the Thai visa exempt program for tourists, so you have to comply with the requirements for this program, and one of those requirements is that you have an onward ticket within the period you are allowed to stay, which is checked at chek-in desk of airline and on arrival (sometimes) at immigration.
What you get on arrival is not a visa at all, but visa exempt, you are granted to stay 60 days without visa.
And when you think Qatar is bad, what is a strange thought, nobody forces you to fly with them.