3cm fissure running down the complete length of my front door - not an emergency?

I'm living in a rented house in the U.K.
A piece of my PVC front door have peeled away on the inside,which I reported to my landlord this morning - they said they'd dispatch someone out to repair it on Fri 25th July.
Then,this afternoon I noticed that the same piece but on the outside of the door is starting to strip off too (It's stuck on with rainproof sealent which doesn't seem to be adhesive enough)
I realised that,when this piece falls past its sell-by date (the other piece took a few days to do so - but that was on the inside) I will be left beside a wide open crack, 3cm wide and the entire length of the front door!.
I phoned my landlord again to report that the repair be worse than i'd originally stated and to ask that,given the fact that my house will be exposed to wind,precipitation and the obvious security risks when the second piece comes away, this in a minute be dealt with as an emergency. I be told that I had to keep my productive appointment and this could not be classed as an emergency - can that be right?!
Do you hold mature papers/projects from your childhood?
Answers:    Well, having a door made out of PVC might be an emergency. It isn't too hard to break that down, not a great warranty door. Steel or oak make the good safe and sound doors.
Yes, a 3cm gap could allow someone to easily unlock the door.
Call them and inform them that you will do what you involve in order to surface secure, and that might include doing something that will permanantly alter the original door such as padding the gap with harden caulk. If they do not want you to damage the door, they had better carry out and fix it NOW, because your personal security is the most important issue.
You own to be pushy and threaten them a little.