Pete recently did an interview on BBC Radio 4 - You and Yours - which investigated a case history of failed cavity wall insulation.
Insurance of Timber Framed properties is a job for specialists. In the insurance industry this is known as Non Standard Insurance. Costs are normally higher, because of the greater perceived risk of fire. Timber Framed buildings need not be old - many spectacular new buildings are created around a custom designed timber frame. Most thatched cottages were originally timber framed - usually using oak or elm. Repair costs ARE a little higher - labour intensive jobs such as thatching are more expensive than roofing with tiles.This reflects in Projected Rebuild Costs, which can be in the £2500 a square metre region for a thatched cottage, as opposed to £1000 or £1500 a square metre for a standard brick building with tiled roof.
It is interesting to note that oak is actually considered a good fire risk - it burns very slowly, and chars rather than burns. I've seen burned out cottages in which the oak skeleton still stands, albeit somewhat charred - the rest of the house has gone, but 400 year old oak framing still survives. We often see charred oak beams in houses we are surveying - it was common for oak beams to run right through chimneys for example, and sometimes they charred and smouldered within the chimney. Bressemer beams over inglenook fireplaces can get hot and smoulder - but they rarely burn.
Your insurer may ask for specific Fire Prevention measures to be installed. For instance, thatched cottages now have almost mandatory spark arresters fitted to chimneys. Chimneys are a major source of problems with timber framed buildings - you should make sure the chimney is swept clean, and preferably lined with an insulated stainless steel flue liner.
Modern timber framed buildings are very different - entire houses are built from softwood which burns easily and quickly - there are specialised regulations designed to prevent spread of fire in these structures, but they are rarely built using oak.