A good reason for the de-pigmentation of skin is resources; IE, it costs the body resources, from the food it eats, to produce the Melanin that gives skin its colour (beyond that of the blood vessels beneath). It's a tiny benefit, but evolution works on such tiny benefits. A person who has less of an uneeded pigment being produced by their body, has more energy to spend on fighting disease/getting bigger/allowing some other bodily system to work very slightly better. Over time, this allows those who have a mutation that decreases Melanin production to outcompete those who still have full-body colouration. This of course is precisely reversed in climes where there is lots of sun, and high intensity UV, as the Melanin will give some protection from skin damage and skin cancers.
A second reason for decrease on skin pigmentation is connected to the one I mention above. Vitamin D production in the body, if not taken in sufficient dietary amounts (and let's be honest, Hunter-Gatherers would be good at getting what they need from food, but it probably wouldn't be a 'balanced' diet and include everything they need to flourish), is only gained from the action of sunlight on the skin. In environments where there is a lot of sun, for a lot of time in each year, lots of Melanin which blocks the sun from penetrating the skin's surface layers, will not be an issue- there's just too much sun to be totally blocked-out and Vit D production os not affected. In Northern European areas, though, the lack of sun will mean that lesser amounts of Melanin will provide that lighter-skinned person with a better chance of producing the Vit D they need. Again, a small change from generation to generation, but a man/woman not suffering from Ricketts is going to be better equipped to survive and reproduce. Freckles might be seen as a sort of evolutionary half-way-house.
So, certainly, as Humanity originated in Africa (from around the Great Rift Valley area, although I could be wrong), the initial waves of colonists, of varying Humaniod predecessor Species, will have been black. I'm not at all sure that there is any evidence that Humans and Neanderthals actually interbred- they were after all a seperate species (but I'll not say I'm 100% certain of this), so I don't think you could place any responsibility on them for diminishing levels of Melanin expression in cold-climate Human populations. However, by the time Humans got to the edges of Europe and into the proto British Isles, the evolutionary benefits of lots of Melanin vs much less would be well into the process of becoming widespread.
It's an interesting hypothesis, and knowing how fast Humans spread, whether by need of resources or just want of exploring, I wouldn't be surprised if Northern europeans were originally dark-skinned. But the reasons for the change from one to the other are well described and well known.