Older homes were usually built with simple shallow foundations, or possibly none at all. They can be vulnerable to movement over a long period.
As older houses tend to be more flexible than modern buildings, they can sometimes accommodate movement without any problem but it may cause cracking, distortion and cause doors and windows to stick.
Nearby excavation or basem*nt construction can be a cause of structural problems.
Foundations are vulnerable to settlement caused by leaking drains, water mains or rainwater pipes discharging straight onto the ground.
A building may be particularly susceptible on clay soils especially where large trees are close to the building. However, whether individual trees are the cause of structural movement should be assessed carefully by a qualified professional. They will be able to provide advice on your options especially as trees can provide benefits too. They can add to the value of your home, provide shade, help cool the environment and absorb rainfall, which will be increasingly important as the climate changes.