Yes and no. The modern Welsh are descended from inhabitants of Roman Britain, but the English are as well. While a few historians and archaeologists still maintain that the Anglo-Saxons wiped out the Romano-British, or drove them all west into what is now modern Wales, most of us now agree that immigants from the Continent mixed and intermarried with the people already living there.

There's a good discussion of the more recent turns of this debate in the first chapter / intro of John Moreland's Archaeology, theory and the middle ages (2010). One of the debates has hinged around archaeological evidence from stable isotopes in teeth (which suggests most populations in England were mixed, of locals and immigrants) and DNA studies of the current English population. H. Härke and a few others have argued that the modern English population's DNA shows they were all originally from the continent, and that that means all the Romano-British were either exterminated or driving into Wales. But most scholars disagree, and say this evidence actually results from much earlier migrations in the Stone Age.

But in fact, the situation was much more complex. In one Anglo-Saxon settlement - West Heslerton, in northern England - there were people who immigrated From the East, locals, and immigrants from Wales into England. The evidence is increasingly showing that this example is the norm, and people moved in both directions during the early middle ages.

So the Welsh are descended from the Roman British people, but so is everyone else south Hadrian's Wall.