in no particular order.
1/. I do not think the builder can be placed on your insurance, because he has no what is called "Insurable interest" in your property, meaning he does not own your home, in a domestic policy you have to own the property you are insuring, for example, I cannot insure your car because I do not have the requisite insurable interest, or, a tenant can insure his / her Contents but cannot hold insurance on the property, it could be granted but when a claim is intimated and it is found out that the tenant does not own the property the claim will be voided and the premiums returned, if fraud is suspected the police are informed and the premiums are retained by the insurer.
2/. As for informing the insurer of the work YES! as far as the insurer is concerned and has been posts above, your premiums are dependant on the area of the property, I work In the Insurance industry, and a lot of the Insurers I work for demand that I work out what is called a Re-Build Cost, dead simple, work out the area of the property and use the tables provided, date of Construction, type of property, Condition and size of the property to get the cost per M2, what happens is that in the above scenario a person purchases say an Ex-Council property, in Scotland for £ 50,000 so they insure it at that value, but that was ten to fifteen years ago, same property now is worth £ 190,000, if the property burns down the insurer will only be obliged to pay out the £ 50,000 not the true-build cost, or if someone puts in a £ 50,000 Kitchen, I inspected one last Friday! but does not inform the Insurer the costly kitchen may well not be covered under the terms of the policy? I saw a property last week that was about £100,000 under insured!
3/. Your Insurer will have provided a route for you to gain access to "Legal Cover" this could, I stress the word Could provide you with legal assistance if you need it to pursue the builder and his PI + PL insurers if the roof collapses and the Builder goes out of business, his PI + PL WILL be valid up until the Builder goes out of business.
4/. Bottom line as has been posted above, A/. Talk to your insurer! B/. Most important, send them an e mail confirming the conversation and get a reply of confirmation. one other thing send them a copy of the builders PL+PI to ensure that your insurer is comfortable with them, at a later date the insurer can not turn round and say that the builders insurances are not valid to your insurer.
5/. In the thread above there is a link to a Specialist insurer who appears to offer cover during building work? I have been in this industry [Insurance] for about 15 years but never come across it before? if you intend using it do a big web search!
Ken