You've got your wires crossed a bit..
As far as you holding a brit passport you can show up here without having bought ANY visa from a thai consulate and get stamped in free for 60 days on the visa exempt entry program
What you're talking about is the TDAC (Thailand Digital Arrival Card) program which started on May 1st.
You can file a TDAC online from 3 days before your travel to thailan right on down to when you're standing in the arrival hall (they have kiosks you use)
This is the website for the TDAC;
*******************************