Waiting times and giving notice

I have been reading about passport waiting times and mine appears to be a bit slower than most. Submitted on 27th Feb, arrived at Hemel Hempstead PO on 1st March but still states the old documents not received. This is a straightforward adult renewal. Another concern is that I am getting married and need my passport to give notice soon- if needed, would it be possible to upgrade to the Fast Track service under these circumstances?