Difficult to draw too many conclusions from that since whilst Jones and Williams are more common in Wales, the vast majority of British people with those surnames are English. Jones and Williams are the second and third most popular names in most of the outer suburbs too. If there's any pattern here it's more likely to be the reverse; the density of very English Smiths is much greater in the outer suburbs.

The nationalistic Welsh will tell you they are the real british people, but displaced and pushed westwards (into what is now Wales) by the Romans, Normans, Anglo Saxons etc. So a name might be mostly Welsh now, but the people with that name might have lived in that area for a very long time,

I'm not sure about this - first-century London was about the size of Hyde Park!

http://en.wikipedia.org/wiki/Roman_London#First_century_AD

Edit - also, it appears that prior to the fifteenth century, the Welsh tended to use a patronymic naming system.

http://en.wikipedia.org/wiki/Welsh_surnames

In the 15thC a Welshman took the throne of England (Henry VII) and brought a lot of fellow countrymen into court with him, so they needn't have been poorer immigrants

Welsh predates english by centuries, in terms of lineage. Most of europe once spoke celtic languages that are most closely connected to welsh.

I'd guess it's because the welsh has a head start on migration of a few hundred years over the other groups on the chart.