Most home insurance policies will include subsidence cover as standard (unless stated otherwise which may be an issue with many insurers if you have had subsidence issues in the past).
Typical practice will involve despatching a qualified professional to inspect damage, which you will probably not have to pay for if arranged by your insurer, and the expert will be able to establish whether or not the damage undergone is covered by your policy.
An excess for subsidence claims is usually applicable. This excess will usually be chargeable to you if and when repairs are undertaken.