The likelihood is that dark skin in the climate and latitude of southern England would be unsuccessful as a dominant trait in the population of the time. Before farming was invented humans lived on the very edge of survival, so anything favourable to surviving up to breeding age (teenage) would be passed on as a helpful trait to the species and any unfavourable traits would be bred out of the population.
Dark skin protects from strong sunlight but does not encourage the absorption of vitamin D as pale skin does, so Cheddar man’s family under these conditions would likely result in contracting rickets with leg deformities, due to vitamin D deficiency. This would greatly hamper a hunter’s success in the field. With limited information about his contemporaries we can’t know how typical the blue eyed swarthy man was, although his DNA clearly remains a component of north-western Europeans. However when farming and cheese arrived on the scene dark skinned people could happily have survived under grey northern skies. Cheddar cheese arrived in the 12th century by the way.
Since at 10,000 years ago it was not long past the time of the recent ice age, you could still walk from Denmark across Doggerland to England. Mammoths would have just recently become extinct on your path but you might have encountered giant elk with formidable two meter wide antlers. There would have been pioneer travellers from the east exploring new living space on the western edge of Europe.
There were however earlier human residents in Britain at various sites so this guy is by no means the oldest Briton. There had been Neanderthals living in the caves at Cresswell in Derbyshire followed by modern humans who carved the walls there around 15,000 years ago in fact the last ice age was the first one which Homo sapiens heroically endured. Strangely Neanderthals, who seem to have been cold adapted, died out before the coldest episode began. The average annual temperature in Southern England 18,000 years ago was -3 Centigrade! (“Ice wedge formations” only occur at or below this temperature and I have seen a number of them locally in pits and quarries in Oxfordshire.)
For the record, The 'Red Lady' of Paviland in Goat cave on the Gower peninsular, near Swansea South Wales, is the red ochre coloured skeletal remains of what we now know to be young man who died about 33,000 years ago.
Cheddar man’s forebears appear to have come from the Near East. In Turkey at this time the Mesolithic nomads were building their remarkable sculptured temple like structures at Gobekli Tepe.