Spig, perhaps you have genuine grounds, but as a generalism I never understand why folk are so keen to slag off insurance companies so readily. I spent many years doing battle with them on behalf of clients and found that they are honourable people and pay up without any problem whatsover, providing of course that they are legally liable to do so. But days of the ex-gratia payments are now long gone.
The cynical might say that there is a massive volume of consumer legislation and regulation, so they cannot really do anything else! But IMHO if all companies were as straightforward as insurers the commercial world would be a far less perilous place. I would trust an insurer above a lawyer any day of the week.
Sometimes folk just seem to jump to the wrong conclusions. I tried to assist one chap who was a friend of a friend who was foaming at the mouth and reckoned he was being "ripped off" by Norwich Union (now Aviva) after a small fire in the kitchen. When I got the details together it transpired that he only insured Household Contents cover - the bulk of the damage was to the fitted kitchen units, insured under the Household Buildings policy by the landlord, who he hadn't informed. Fitted kitchen units are always considered as part of the building and so claimable under the buildings insurance. He had been told this by Aviva, but didn't want to know.
The "cooling off period" is purely to comply with the Distance Selling Regulations and not connected to the cancellation of the policy in the situation indicated.
Nitram, the policy will show details of the cancellation terms. It will normally be a table and generally the maximum return will be 75% or so of the premium within a month on a decreasing scale. Your friend is best off to read the policy first, then speak with the insurance company. If there is any problem do send me a PM and I'll be pleased to assist if I can.