My chimney sweep has told me that for insurance purposes I need a safety certificate if I have an open fire in my flat. Is this so, and what is involved?

If you are installing a new open fire or converting a previous gas fire back to an open fire then you are subject to the building regulations, Approved Document J is the guidance and a check list and certificate are involved Check out http://www.planningportal.gov.uk/buildingregulations/approveddocuments/partj/approved and your local building control.