After my insurance claim experience with a cheap insurance company when my flat roof was blown off in Storm Arwen, I would recommend looking at the Which page which has approved home insurance providers. They did the customer surveys with people who had claimed.
From memory, LV, John Lewis and Tesco are near the top of the list. Have a look.
They will be more expensive than the 'comparision' site insurers, but hopefully that is because they have a 24/7 telephone line, enough loss adjusters, and enough workers to fix any problems. The company I was with, cheap, had none of these and I waited three weeks before anyone was sent to do a makesafe. In that time my lounge ceiling came down. I was ten weeks without a roof before anyone was able to fix it.
Once you've found someone you like, have a look at their 'bad' reviews on TrustPilot. When you've chosen and complete the form for a quotation, do ensure you put the correct percentage of flat roof on your property ie 20-30%, 30-50% etc.