Our last house had to be underpinned - not all of it, just the front bays which were cosmetic extensions added in the 60s with poor foundations. This had been missed by the survey - but that's another story. We'd lived there for 3 years before we realised there was an issue and had it underpinned.
We had to go to specialist insurance but it was considerably cheaper than our previous insurance! We queried this and was told was that the underpinning had made the house 'rock solid' and unlikely to have any further issues so was a low risk. Also they said the reason you have to go to specialist insurers isn't as negative as people think, most grade II houses etc have to have this as well, due to the fact that most 'high street/online insurers' don't have enough knowledge to assess the risk. Our specialist insurer was recommended by our previous insurer and they were really good.
We had no trouble when we came to sell it two years ago. We had the underpinning done to a high standard, the previous insurance paid for it but then referred us to the specialist insurer, we had all the paperwork, got a survey done post completion etc so I would ask to see all these.
The buyers surveyor told them he had no issue with well underpinned houses if all the paperwork was there and also underpinning meant the risk of any further movement. Most older houses, particularly in certain parts of the country, are subject to movement . Also whilst you can change insurer if you buy the house, legally the current insurer has to continue to provide insurance and can't decide not to