Matthew, all I can say is patience. 3-4 months maybe.
I know someone who was called for the AFCO for a naval interview. They came away with a fountain pen that said Naval Officer.
They later had an interview with the RAF.
A letter was received from the RN 3 days later with a 1st class stamp. By the end of the following week a phone call to the RAF elicited the information that a letter was in the post. It arrived the following week, 2nd class post.
I know another who was fobbed off for 6 weeks as the interviewing officer was posted.
Note the underlying points.