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.