I don't know about Crofton Park/Blythe Hill specifically, but any older property in SE London has a risk of subsidence, given it's clay heavy.

My understanding from another poster here on an earlier thread (I forget which) is that insurers will generally assume a potential risk based on your postcode - so the whole of SE23 is relatively risky for example.

Get a proper survey of any house or flat you buy if it is in an older property (especially if its a victorian terrace, as they have shallow foundations) and make sure your solicitors ask the seller if there there is any history of subsidence with the place as part of their enquiries. The major cost with subsidence is when it happens to you and you have to claim under the insurance - you basically get stuck with your current insurer (the major insurers wont newly insure a house that has had a subsidence claim in the last 10 years at best) and your insurance cost will go up.

There is no insurer that wont add a premium - the problem is finding one prepared to insure it if there's been a claim. If your house gets underpinned, then (fairly or unfairly) you will generally find only niche insurers such as NFU Mutual will insure it. Although, as an NFU customer out of choice (no subsidence with our place!) they have been very good so far...

Hope that helps.