Mine was printed on the 12th and it is still waiting to be picked up – I was told there was delays due to the bank holiday but would have expected it to have been collected by now given it has been 6 working days!
I didn’t get any notification of dispatch after my passport was printed on the 19/04 (just a schedule for delivery today text from TNT on 21/04) but I managed to track the delivery through the TNT delivery services page myself.
First by entering postcode and application reference (PEX number). This shows you the TNT reference number which you can use to track the delivery. Note that initially I was getting an ‘invalid’ message against the application reference which I assume meant that the passport had not been dispatched/picked up by TNT yet.
For those without TNT tracking or if its not working, another provider might have been used. I received my passport today via DHL, only got the text this morning with tracking information. It’s totally different to your PEX number and it was UK mainland delivery.