I know this is a sort of advert - but I hope it doesn't breach rules.
In case anyone else has just seen the shock premium increases from FirstAssist, you may be interested to investigate Standard Life's Healthcare policy. They are prepared to take on risk from existing policies on a full medical underwriting basis with no exclusions. The key obstacle or reason for staying with the IBM scheme - ie acceptance of any existing condition or condition that emerges is therefore removed. The key difference to their policy is that they also offer up to a 50% no claims bonus which you can claim straight away. So the premiums appear to be half the price for what seems broadly similar cover.
Hope it's useful