I know we all complain about how long it takes Monzo to process cheques (how long is it these days) but First Direct ughhh.
They used to be so quick. Post Mon, arrive Wed, credited Wed. Now it’s been more than a week and not a peep.
(Yes I know I could just go into branch)
Don’t they have cheque imaging via the app?
HSBC (the parent bank) does.
Unfortunately not 
That is a long time. You should definitely check they’ve actually got it in the system.
I worked somewhere where cheques are received/processed and I can tell you that after the various stages and checks that each credit goes through, a very small number of them are missing and turn up in the bin or in some random place due to human error (stuck to the envelope, or gone with the wind).
That’s not even taking into account all the letters that end up on a pavement or in a gutter from the postal system before it even arrives at the bank 
Definitely chase that one up.
And that is why we should have cheque imaging!!
The cheque did eventually arrive, about 10 days after posting. I think First Direct are just getting a bit slower at processing.