Native trees are species that colonised the British Isles after the last ice age.
The term "native" tree has a fairly precise meaning when applied to the British Isles. It is a species that colonised the British Isles in the period 10,000 years ago to 6,000 years ago - in other words the period after the last ice age ended and the climate started to warm, but before rising sea levels formed the North Sea, Irish Sea, and English Channel and finally cut off the UK from further natural colonisation.
While this colonisation process was mostly achieved by natural dissemination of seeds, the first humans settlers arrived at this time, bringing with them plants and trees that they found useful - so even from the start human activity has influenced our native trees.
The Woodland Trust list of British native trees is considered the best reference point for native trees.
Some of these species have been subsequently shaped by human activity, giving rise to cultivars and sub-species. This is particularly the case with Prunus and Malus, both native to the UK, but where since prehistoric times man has selected and cultivated and propagated cultivars with larger and more palatable fruits. However in the last few centuries there has also many new cultivars of ornamental species have also been developed for their aesthetic qualities.
It is perhaps debateable whether these modern cultivars are "native", even if they have been cultivated from a true native species.
We take a relaxed view that modern cultivars which do not stray too far from the parent native species in appearance can be considered native. On this basis a James Grieve apple tree is not native, but a Sorbus 'Asplenifolia' (essentially a more colourful form of the native Rowan Sorbus aucuparia) probably is.