Why trees matter on clay
Trees draw moisture from the soil. Clay soils shrink as they dry and swell as they wet — heave and subsidence. A foundation that is too shallow inside the influence zone will move.
The NHBC tables
NHBC Chapter 4.2 sets out minimum depths based on tree species, distance and clay shrinkability. Building Control will check the foundation depth against those tables.
Trees you cannot see yet
A neighbour planting a row of leylandii after your extension is built can still affect your foundations. Long-term thinking matters here.