Climate change is expected to be a gradual process so trees chosen to meet current conditions of soil and site should be able to withstand changes for many years. The RHS Find a Plant is designed to help choose plants well suited to current conditions.

However, if they are not entirely suited there is a risk that they will succumb as marked changes occur. If a tree unsuited to a well-drained sunny position is planted on a south-facing slope where the soil is sandy it will usually grow satisfactorily now, at least in years of reasonable rainfall, but will suffer in droughts. As summer droughts are expected to be more common and more severe in southern and eastern areas, such a tree would be at risk in the future. 

Beech trees, important in forestry and grown in gardens (although a little large for most gardens), are a tree ill adapted to these dry conditions and therefore not a wise choice in southern and eastern Britain. Oaks and ash are likely to be better adapted for future forestry needs. Scotland and other northern and western regions will probably become more hospitable for beech.

The situation is less clear for garden trees, but there are some recommendations that can be made.

Drought impact: Drought crack is likely to increase in England and to cause defects in timber. There is likely to be a greater risk of trees spontaneously dropping limbs. Gardeners are liable in law for damage arising from trees and should ensure their insurance covers damage from trees.

Waterlogging effects: Subsidence could also increase as wetter winters swell soils and dry summers lead to trees extracting more water than at present leading to damaging soil shrinkage.

Warmer and wetter winters: These could lead to more active root pathogens, so roots will be more seriously damaged. Then, when the root systems come under stress in the hotter summers, more trees and shrubs will die.

Using Mediterranean and exotic trees: Planting stock adapted to hotter, drier climates represents a possible adaptation response to climate change. However, they may suffer from unseasonal frost damage as occasional cold winters remain a possibility despite climate change, although potentially rarer than at present. Exotic trees, such as evergreen oaks or eucalyptus would alter the character of gardens and landscapes.

Trees tolerant of hot, dry conditions

Trees planned for free-draining, south-facing slopes in southern areas are likely to suffer from hot dry summers and prolonged drought in future. The following are suitable; 

Small trees:
Crataegus crus-galli: Small spreading deciduous tree to with long thorns.
C. × persimilis ‘Prunifolia’ AGM: A better garden tree and almost as resilient. 
Juniperus scopulorum: A small conical coniferous tree, with reddish bark,
and bright blue-green foliage. Almost as robust and better for garden use is J. scopularum ‘Skyrocket’ whose spectacular narrow form is a welcome addition to many gardens.
Gleditsia triacanthos: The yellow leafed cultivar ‘Sunburst’ is best for garden use and has the RHS AGM, with bright yellow young leaves ageing to light green by late summer, and is significantly smaller than the green leafed species. 

Medium trees:
Catalpa speciosa: Not widely grown but has considerable potential for dry conditions, but has similar foliage and flowers (although more sparse) as the common but not particularly drought tolerant C. bignonioides. 
Eucalyptus pauciflora subsp. niphophila AGM: A particularly hardy evergreen tree noted for its attractive flaking colourful ‘snakeskin’ bark. However, eucalyptus have been frequently implicated in subsidence and gardeners should be wary of planting near buildings. 
Ginkgo biloba AGM: A robust deciduous tree with striking foliage. Female plants produce fruits which can be a nuisance in autumn. Male plants are trouble free.  
Koelreuteria paniculata AGM: is grown for its yellow summer flowers followed by bladder like fruits. 
Pyrus calleryana: A very robust deciduous tree widely used in landscaping. The cultivar ‘Chanticleer’ has the RHS Award of Garden Merit with a neat conical habit making it suitable for large gardens. 

Large trees:
Cedrus atlantica: A large conifer, conical when young and spreading when taller. The blue leaved form ‘Glauca’ has the RHS Award of Garden Merit and is especially spectacular as a specimen tree for very large gardens and public open space.
Quercus ilex AGM: A large spreading evergreen with attractive green foliage that is suitable for the largest gardens and parks. 

Trees tolerant of waterlogging:

Small trees:
Prunus padus: A small decicuous tree with striking flowers and young foliage and shoots. The cultivar ‘Colorata’ has the RHS Award of Garden Merit and especially attractive pink flowers followed by dark fruits. 

Medium trees:
Alnus glutinosa
Betula pubescens
Salix alba: A compact medium sized tree that is very tolerant of wet soils. Two cultivars that have the Award of Garden Merit are S. alba var. vitellina 'Britzensis' (m) AGM with coral coloured young stems and S. alba var. vitellina AGM with bright yellow shoots.

Large trees:
Acer rubrum: A large spreading deciduous tree with remarkable autumn colour. The cultivar is an especially valuable tree for very large gardens and parks: 
Taxodium distichum AGM: A large deciduous conifer that is fairly tolerant of drought as well as very tolerant of waterlogging. This tree has an Award of garden Merit but is really suited to very large gardens or public open space. 

Link

RHS Find a Plant