British don't get visa on arrival. British can enter Thailand without visa for a stay of 30 days that can be extended once for 30 more days. Outbound ticket is mandatory though.
I extended my non-OA visa and yes, for the first application they wanted a bank document showing the money came from abroad, they came to visit my house too. But for the subsequent renewals they just wanted to see my bank book with balance certificate and stamped my passport the same day.