Immediately before Roman times Caesar regarded southern Britain as an extension of Gaul, with political and dynastic alliances well established between both and constant two-way traffic of goods and people. This was how he justified his own incursion into the region - reckoning that as long as the British tribes were not brought to heel it would be all the more difficult to subdue those in North Gaul. It is generally presumed from this that they spoke more or less a common language too.
However the author of the website above is right, I think, to challenge this view and suggest that in fact southern Britain was prone to different linguistic influences at the same time based on geographical proximity to the different sources of the day. Just as the Gallic distribution of languages was much more complex than Caesar noted at the time, it would be logical to assume that the same pertained on the large island which formed a part of this network, especially if mobility and interaction between its inhabitants and their continental neighbours was as extensive as everyone now seems to agree it was.