To echo what others have said, if it gets to 48 hours get to your passport office and they will prioritise you (from what I saw this is the case even if you are within six weeks).
A lot of people in the same boat but they get through them. Arrived at 6, but needn’t have bothered, close to 8am would have been exactly the same time seen, with approx 40 people waiting today at Peterborough.
I have seen a couple of people mention that theirs had been processed under the standard method and not upgraded and it was awfully close to their departure date. This was the same for myself and Neither the passport office or TnT were saying they had the document. After no initial luck this morning I went back to the office and explained the issue to the entrance staff, who passed my details direct to the processing team upstairs .
They contacted me back within an hour and resolved the issue within the day.
So if there are still others in a similar position playing the waiting game for TnT, if you don’t have a delivery date or tracking number yet I would get down to your passport office and explain the issue. They were brilliant!