As the photograph shows it’s not always large trees that can cause problems.
Trees and other vegetation too near a building can damage a structure and its services, particularly when the sub soils are clay based as they are in this locality. Roots can cause shrinkage as they search for water, particularly in dry weather. You should employ a competent tree surgeon to pollard (thin, prune and shape) nearby trees now and then periodically to maintain their condition and restrict further growth.
Trees are an integral part of the environment. It is always important to consider the balance between the species and location of the tree. Inappropriate species planted near to a building should be avoided. There are no hard and fast rules for assessing the risk of damage that tree growth close to a building will cause as there are many variables involved.
If in doubt it is sensible to seek advice specific to your site from a qualified and experienced Arboriculturalist (tree surgeon). A regular programme of pruning will keep the aesthetic shape of the tree, restrict leaf growth, root spread and consequently moisture demand. Remember that a mature tree could be the subject of a Preservation Order and Local Authority consent may be necessary before starting work.