You sound like you have a "cold" flat roof (the other is a 'warm' where the insulation is between the rafters).
The actual flat roof has probably been replaced (they have 20 year lives if installed correctly). But it is worth checking how it was done. It may be just a roll with one layer.
Some flat rooves such as mine are three layers which are burned / melted onto one another, with the cavity between the rafters empty except for electric cables. This is where the actual bitumen on the flat roof acts as the insulation. It can be very effective.
If yours is the original flat roof then I suggest you replace it. It is probably near the end of its useful life and replacing with a modern type could bring significant savings. It may be your responsibility or the freeholders (in which case it will be charged back to you .. and a scaffold to the second floor will cost you £2000 ... the roof maybe only £1500).
You may be eligible for support from energy companies through the energy company obligation.
Filing the cavity sounds like a good idea, but may have issues with electrical cabling and fire safety. If the cables are old, they could cause a fire and the insulation may just burn. I knew a couple who were watching TV one evening and felt hot ... they went to turn down the heating, then get a fan, then the next thing they knew was a fireman burst through the door and dragged them out ... they didn't realise their roof was on fire for 30 mins before the fire brigade arrived.
You want a surveyor or expert who can advise you how to do it in a safe way. And probably rewire at the same time.
https://www.nia-uk.org
Try the NIA and speak to three people ... one will not show up, two will come and you can see who knows the most.
Good luck !
