Leak from Upstairs Flat

Maintenance

Hi, I've just been told this morning by my tenant who is on the 1st floor that water is coming through the ceiling above in 3 of the rooms. I have spoken to the property managers (managing agents for the flats) and emailed them before 9am and spoken to them at 9.30am about the leak. They said they would get in touch with the owner and get them to call me so we can sort this out between us. No one has contacted me yet and it's 18.15 now.
I found out that no one has lived in the upstairs flat for 2-3 years and what worries me is they are abroad and/or are uncontactable.

From the way the leak has presented itself, it seems a slow leak where the water has probably been collecting above the ceiling and has now found avenues. I certainly do not want the ceining coming down and causing injury.
I also asked the managing agent about starting an insurance claim twice, which they have ignored so far.

Does anyone have experience and advice on what my actions should be and what I am allowed to do to speed up a remedy. For example, I need to make sure the water upstairs is turned off ASAP.

Any information would be most welcome.