Our house, which is down the road/hill from CP, had subsidence. It is a bit of a SE London problem. Personally, I wouldn't necessarily rely on the replies from the seller - they could legitimately be unaware of any problems. Caveat emptor! Do you own due diligence. We got a full structural survey. If there is a hidden problem then it is easier to sue your surveyor than the seller.

Quite a few mainstream insurers don't insure this area (apparently), but lots of others do. If you find the place has had subsidence, don't worry! We got insurance from an alternative insurer at a massively reduced rate (compared to the original insurer's rate). It's via a specialist broker company in Maidstone: http://www.woodstockinsurance.co.uk/ I am sure they'd give you a quote, so you can see what you are getting into. One thing to consider is the excess on the policy - our mortgage company stipulated a relatively small excess, which we only realised just before exchange!

Don't be put off! It's a great area to live in. The wonky angles in our house give it more character ;-)