Jessica, I have got mine today. The timelines as follows:

Sent: 1 Oct
Acknowledgement letter dated: 3 Oct
Passport returned with PSW visa: 13 Nov.

Around 6 weeks in total.

Good luck with yours.

jessica,
my dates are exactly the same as yours, have not received it either. perhaps it is a busy month for HO.
please let me know once you have heard anything from HO.
ff

this is super-fast. congratulations!

has anyone received their passports back with approved leave to remain under PSW during the past week? If so, how long has it taken in total?