Insurance companies as a whole will try to avoid paying out if they can but are happy to take your money. Some cover is more comprehensive than others so is always best to shop around and read the small print so to speak.
Basic public liability in general don't normally cover property being worked upon etc which is no good if you happen to damage whatever you are cleaning at the time. You also have to make sure you are covered for all the services you offer and never assume you are. After saying that unless it's written into the policy doc you will not be covered.
Recently I damaged a conservatory roof I was cleaning at the time. Turns out the roof panel which was damaged can't be replaced as they don't make that type of plastic panel anymore nor any supplier stocks them. Only other option is to replace the whole roof which I'm so glad I was covered as would have been very expensive to do.
Just goes to show that we can all make costly mistakes so best make sure you are covered properly.