Our house is underpinned. My husband is in property insurance and says he'd rather live in a house that has already been pinned as there's less chance of something going wrong! We got a full structural survey from a specialist surveyor nonetheless. He was amazing!
Make sure you ask for as much info about the work as you can from the sellers and get any guarantees. I checked out the company who provided a guarantee on our house to make sure they were still solvent.
With insurance, it can depend how old the work is. If it's more than 15 years you may not have to declare it (check the wording carefully). Also check whether the mortgage company has imposed a particular excess as a condition on the mortgage. Our mortgage company wanted £2k, whereas the insurers wanted us to pay £2.5k so we would have been in breach of the mortgage unless we'd spotted it. We use a specialist broker in Maidstone and our premiums aren't too bad. We couldn't go with the previous insurer for a number of reasons, including the fact that it was Notthern Rock!
Good luck!