Alas, Cheddar Man duped even the likes of me.
Cheddar Man was a Mesolithic hunter-gatherer, not a Neolithic farmer, and the very dark reconstructions on him were an artistic liberty taken with him lacking many of the alleles modern Europeans have associated with depigmentation in mind. The media picked it up and ran with it for political reasons I would get banned from this website for talking about, but that's another tangent for another time. The Atlantic Neolithic megalith-builder inhabitants of Britain that seem to have flooded Britain relatively quickly from the continent in a few generations and were finally almost completely wiped out by a paternally-Indo-European Bell Beaker-era invasion lived thousands of years later and were of a very different genetic stock to Cheddar Man. Depigmentation widely happened across Europe during the Neolithic and also literally everywhere else intensive agriculture spread in a higher latitude - in Asia, East Asians developed and selected for a variant of the OCA2 gene that causes skin depigmentation, which is why a lot of Chinese, Koreans and Japanese are paler than Cheddar Man could very well have been. In fact in Europeans another variant of OCA2 plays a part in blue eyes, the eumelanin in dark eyes is the same compound as the eumelanin in dark skin so this shouldn't surprise us.
Now, the article you read would probably have told you that Cheddar Man and his ilk (Western Hunter-Gatherers) were actually the original population with blue eyes, so why dark skin? The dominant theory everyone has read about is that it was selected for due to dietary folate and vitamin D levels - if you have an early agriculturalist's grain-based diet, you need to synthesise more vitamin D yourself and you have an excess of folate (which UV exposure causes to degrade in the human body) . Without animal foods that are rich in most nutrients, at a cloudy higher latitude and with way too much folate in your blood anyway, it's probably evolutionarily advantageous to not have a high concentration of eumelanin in your skin (polite way of saying be pasty to avoid rickets). People have argued sexual selection for lighter skin but that doesn't even seem to be 100% universal in humans so who knows, and it seems mainly to apply to completely separate agricultural people in mid-high latitudes so while I'm not a biochemist something to do with diet makes sense to me. I imagine Cheddar Man as maybe having an Inuit-like ruddy-brown skin tone personally, since those people live at a high latitude and have always been hunter-gatherers with a high intake of animal foods. Agriculture makes their East Eurasian relatives and Cheddar Man's West Eurasian mid/high-latitude descendants much paler as a rule.
Diet is responsible for other characteristics of Neolithic Europeans too, by the way. Gravettian Paleolithic Europeans were some of the tallest pre-industrial humans ever to have existed, but a nutrient deficient, grain-heavy, tooth-rotting, bone-stunting agricultural diet so selected for conserving nutrients and calories that Early European Farmers became very short. Males of the Funnelbeaker Culture in late Neolithic Northern Europe who were about 50% Hunter-Gatherer by blood were still like 160 cm tall. It's not really outlandish, countries of short people who have a genetic predisposition to being short exist today like Peru, Indonesia, etc. And also the southern regions of Europe like Sicily, Greece, Southern Italy and ESPECIALLY Sardinia where Indo-European blood didn't penetrate as much are the shortest in Europe, again for genetic reasons, owing to their high amount of Neolithic farmer blood. Sardinians are especially interesting since they have very little Indo-European blood, were never really invaded by IEs until historical times (when Rome conquered the nuraghe-builders), and on PCA charts of population genetics their alleles tend to cluster closest with the original Neolithic farmers from Anatolia. (much closer than the current inhabitants of Anatolia actually! Being isolated on an island with no prior inhabitants for thousands of years helps!)
Steppe Herders had a diet much higher in protein and nutrients from animal products than the local farmers. Neolithic Europeans had pastoralism too and made cheese, but Steppe herders were on another level - they were in the process of selecting for lactase persistance, drank the milk of cows and horses which they spread far and wide, rode around on initially wagons and then famously chariots, and their arrival coincides with (not pointing any fingers!) general deforestation as they cleared large tracts of land to raise their livestock. Archeologists have determined (based on ancient pollen samples and other stuff left in the soil, I imagine) that when the Corded Ware Culture rocked up in Jutland they deforested the entire peninsula really quickly. Lactase persistence isn't unique to Europeans either, it's developed a few times in the Sahel region, one other time in the Middle East and also in dogs domesticated by Europeans to my memory, but in Europe it's famously widespread. Steppe Herders did not have much of a history of settled agriculture at all when they arrived in Europe - the Western Steppe Herder population is a mix of Eastern Hunter-Gatherer-derived males of Russia and females from the Caucasus they took as wives. It showed in their appearance - they were big, physically powerful individuals with an appearance not at all characteristic of a population suffering from a nutrient-deficient grain-based diet.
The prevalence of light hair and eyes across Europe might actually be their fault though - it increased in frequency in a way people studying the Bronze Age and human populations have really struggled to explain. There was definitely positive selection for light hair and eyes in Bronze Age Europe, and unlike skin pigmentation these things don't seem to have much of a benefit for survival/nutrient levels in a high latitude. It's definitely unique, especially considering the alleles for blondism (which one associates with blue eyes) came from a completely different European Hunter-Gatherer population further east of Cheddar Man, and they were combined in this package by later migrations and invasions. Some people have proposed that it might actually be just cultural sexual selection, and to do with Indo-European "chieftans"/local kings selecting paler women, then breeding more and their offspring having higher status and thus a higher likelihood of breeding for many generations. The propagation of Indo-European paternal lines across the population over many generations thing definitely happened - modern Europeans in Atlantic countries are majority Haplogroup R1b. The majorities of entire nations can trace their direct paternal lineage back to just one dude who lived 5,000 years ago. I'm R-L21 myself so this applies to me. This even applies to places like Iberia/Basque Country where Indo-Europeans came late, as a small contingent, and didn't even get their language to stick most of the time (see: Pre-Roman Iberian language isolates)
So if they had a cultural preference for breeding with pale women, maybe they could have done it. Indo-Europeans were very patriarchal, customarily sent out young men in raiding parties and we can even reconstruct their word for "bride-price" so their head honcho and his sons could definitely pick the women they wanted out of a subjugated population. Places where Indo-European invaders and their genes make up a higher proportion of the population's ending up having high frequencies of light hair and eyes, much higher than the original Yamnaya themselves and in most of the farmers they subjugated? This is the rule in Europe. And I don't think it's just pop-prehistory how macho they were (Gimbutas's Neolithic matriarchy idea definitely is), they probably had traditions that made Kyrgyz bride-kidnapping look like a suffragette demonstration.
I think all of these things could be food for thought as to what Europeans at least might look like without an Indo-European invasion (since we can't really speak most of their languages, of which there were many, or ask them about their culture instead of consulting skeletons and pots). I think these alt-Europeans would be short, gracile people, with narrower frames and lighter bones. They'll have pale skin like Europeans in real life, but a much lower frequency of light hair and eyes outside of isolated places (so they'll have dark hair and eyes). Not sure whether they'd be more dolichocephalic or brachycephalic than modern Europeans or what other aspects of their facial features might be like, hopefully someone else can comment on that since average skull shapes in Europe seem to have changed since the Bronze Age for reasons not directly related to Indo-Europeans. Their faces will definitely be recognisably European though, as IRL Sardinians' are. Nothing freaky. They might be mostly lactose intolerant, or the prevalence of lactase persistence might be much more geographically limited in Europe than in real life, but they'll eat cheese like Europeans in real life do. If someone from this parallel universe was transported to ours and started walking around the street, you wouldn't notice much besides their bewilderment.