For most of these cultures, "cities" did not exist, and even assuming they did, from the times of the first early-agricultural settlements, might have numbered a few thousand, perhaps tens of thousands of souls. With little transport, food was either sourced locally, or brought in on boats, rafts, or barges. Total collection areas for bulk goods of more than a few kilometers would be highly unlikely, though longer trade routes for rare materials (timber, metals, spices, hides) might have existed.

A principle relic of such settlements are their rubbish tips. Again, lack of transport meant that waste and filth were moved a few meters, for as long as the settlement existing -- decades, centuries, or millennia. In many places these are the principle evidence of early settlements, particularly shell mounds (shellfish are an easy, reliable, and sustaining prey), and can themselves measure several meters high and tens of meters across, particularly on otherwise flat aluvial or riparian landscapes.

The TLDR is that a huge low-lying basin of fertile land around what is now the British Isles was inundated at the end of the last interglacial. (What is now the North Sea/English Channel was one of those river valleys you alude to.) The British Isles today would have been the relatively cold, arid, mountainous uplands survivors migrated into when their fertile, low-lying territory got flooded out. Assuming population density in the chilly uplands (glaciers, remember!) was low, then you'd expect the frequency of surviving stone tools to be lower, reflecting that. People don't leave stuff lying around in places where people don't live!

There are plenty of very fertile, habitable areas in the same region that would have been just as attractive. So settlements? Sure. But surely a civilization is more than just a settlement?