Duckling - your information is not quite correct. If a building has a past history of subsidence, the insurer at the time of the subsidence is obliged to carry on insuring the property, even to subsequent owners. It does mean that you have no choice of insurer for some years. After twenty years from the date of the subsidence, if there has been no further movement, you can usually go to the market (but you need to speak to insurers directly, rather that doing it online). So it's not entirely true to say: 'the problem is finding one prepared to insure it if there's been a claim' because the original insurers will insure it in the short to medium term and eventually other insurers will too.

Also, if you suffer subsidence and you claim on your insurance, that doesn't necessarily mean your premium goes up. I had serious subsidence in a house in East Dulwich. I claimed on the the insurance. I had to pay £1000, which was the excess on the policy, but £40,000-worth of work was done. My premium did not rise.