My application is also now showing up in the HMRC app as "completed" - received on 2nd September, posted a week before.
A difference from most others here is that I did it without receiving the letter
Apart from the initial approval of years, I've never got anything in writing from them, but have instead just made extra yearly payments and had them accepted. So followed the same logic and all seems well... I hope completed means accepted!
A difference from most others here is that I did it without receiving the letter