Update
I got my daughter’s passport! I ended up buying a cheap one way flight to Toulouse for Wednesday and then went down to my local passport office (Newport) this morning. We were there about 2 hours before it opened but there were still several people in front including someone who had been told to travel from London to Newport!
Anyway, we filled out a form and they promised to call back today. An hour or so later, I got a call from Belfast who wanted confirmation of the flight which I emailed. Belfast rang back two hours later to say that the passport was being printed there and then and to come and get it when we wanted. I made my daughter go down there straight away but I didn’t breathe a sigh of relief until it was in my hands.
They will not print a passport unless you have only 48 until the flight but you don’t have to go to the passport office where the application has been sent.
Hope this helps people.