My house is more than 50% flat roof (due to a large extension). Many insurance providers don't seem to quote at all if the flat roof is >20%.
Any advice on where to get cover at a reasonable premium?
Did you try Allianz? They might do it.
I had big problems finding an insurer for my place some years ago due to the age of the house- it is well over 100 years old. Allianz was the only one who offered me the service. All the other insurers refused.
If possible, it would be handy to know the actual pitch of the roof.
Check if the insurers have a definition of a flat roof and see how that compares with what you actually have.
Not all flat roofs are necessarily flat for insurance purposes.