Thanks, I've added it! British English is kind of our weak spot. Let us know if you notice any other missing Britishisms.
Righto. I'd be interested in helping out more broadly with translations into (British) English from any Duolingo language if that would be useful.
I usually report and / or comment if there are British words missing where American words are accepted and I get voted down for it.
"checkout" is also reasonably common in British English, but indeed "register" isn't
I'm British and often lost with American translations, especially Major which is an army rank or the opposite to minor. In the case of paying in a shop, surely the Cash Desk is readily recognised in all dialects of English.
If you said "cash desk" to most people I know, they would understand. However, there would be a moment of confusion or a blank-stared "mental gears turning/circuits beeping and booping" as they translated it.