You can find all the native British trees listed here, and we grow and sell most of them. This list includes all the trees & big shrubs that are considered native.
The definition of native trees:
"True natives trees" are often defined as:
Trees that colonised Britain during the time between the end of the ice age about 10,000 years ago and the formation of the Channel by the gradual expansion of ancient rivers, some thousands of years later.
Trees that came after the Channel had formed are generally called Naturalised.

List of Native British Trees & Shrubs

Plant GroupNative Trees in the Group"True" Native Tree?
AlderAlnus glutinosaYes
AshFraxinus excelsiorYes
AspenPopulus tremulaYes
BeechFagus sylvaticaNo (Probably brought by stone age humans)
BirchDowny Birch, Betula pubescens & Silver Birch, Betula pendulaYes
BlackthornPrunus spinosaYes
BoxBuxus sempervirensYes, South GB only
Buckthorn

Alder Buckthorn, Rhamnus frangula - Purging Buckthorn, Rhamnus cathartica & Sea-buckthorn, Hippophae rhamnoides

Yes
CherryBird Cherry, Prunus padus & Wild Cherry, Prunus aviumYes
Crab AppleMalus sylvestrisYes
DogwoodCornus sanguineaYes
ElderSambucus nigraYes
ElmEnglish Elm, Ulmus procera - Wych Elm, Ulmus glabra - Smooth-leaf Elm, Ulmus minorYes for Wych Elm. The others are disputed & only in the South.
HawthornHawthorn, Crataegus monogyna - Midland Hawthorn, Crataegus leavigataYes
HazelCorylus avellanaYes
HollyIlex aquifoliumYes

Hornbeam

Carpinus betulusYes, Mostly South GB
JuniperJuniperus communisYes
LimeLarge Leaved Lime, Tilia platyphyllos & Small Leaved Lime, Tilia cordata

Yes, South GB only.

MapleAcer campestreYes, Mostly South GB.
OakCommon Oak, Quercus robur & Sessile Oak, Quercus petraeaYes
PoplarBlack Poplar, Populus nigra & Aspen Poplar, Populus tremulaYes
Rowan a.k.a Mountain AshRowan / Mountain Ash - Sorbus aucupariaYes
Scots PinePinus sylvestrisYes
SpindleEuonymus europaeusYes
Strawberry TreeArbutus unedoYes, Ireland only.
WhitebeamSorbus ariaYes
Wild Service TreeSorbus torminalis Yes
WillowGoat Willow, Salix caprea - White Willow, Salix alba - Crack Willow, Salix fragilis - Salix triandra - Salix pentandraYes
YewTaxus baccataYes

Although Britain has many native trees, there are effectively no endemic trees, i.e. trees that are native here and nowhere else. If all the trees in Britain were destroyed tomorrow, the world would not lose a single distinct species of tree. The small exception is a handful of asexual micro-species of Whitebeam, Sorbus aria. These apomictic plants are a bit of cheat if they want to be held up as unique: they naturally occur in Whitebeam populations around the world and each strain only counts as a distinct species because they reproduce by cloning only. They are in all other respects the same as normal Whitebeam, so they are not of any special importance to an ecosystem.