Subsidence in 1960's home (sale completed only yesterday)

They are responsible. You can claim through their professional indemnity insurance.

Contact the estate agent that sold the house

The surveyor should have picked up on this and it should be in the report. It may be foundations or soil shrinkage that is the cause but could potentially just be long standing movment. You can ask your own structural surveyor to give you a report but a structural engineer would have to officially confirm it as subsidance. If it can be confirmed you can complain to the first surveyor, it may be worth speaking to a solicitor as to what they can be held accountable for cost wise. Lastly as a note all morgages and loans have a 14 day cooling off period, you may withdraw from the loan within this time.

If you only had a basic survey for the mortgage you won't be covered! Only with a full survey

Hi there, I would not make an assumption of subsidence straight away. Are the cracks anywhere near windows or external doors. There are other reasons for movement that may include but are not limited to building or structural interventions, general movement and settlement. There is also a chance of heave. It is fairly uncommon and your surveyor when doing a mortgage survey would have checked local ground conditions but this survey is generally quite cursory. Your buildings insurance company would be aware of your home being in a subsidence prone area and would perhaps reflect this as a specific within your policy. I would bite the bullet and get a structural survey done of the house and/or indicate the problem to your insurers who may provide you with a surveyor.
good luck

Underpinning the exterior foundations where required would solve any issues