The Welsh never spoke Gaelic, Wa-Na-Be. The Welsh speak Welsh.
There are three branches of the Celtic languages in the British Isles: Gaelic, which is Irish and Gallic (Scotland), Briton, which is Welsh and a related language spoken in parts of Brittany, and Manx.
The Cymru speak Cymraeg. The word "Welsh" means foreigner in Anglo Saxon. What happened to the "Welsh" has many parallels to what happened to the indigenous peoples of North America who were and still are considered to be foreigners in their ancestral homeland. The Cymru consider the name "Welsh" to be as offensive as Red Injun might be to a Seneca.
And it is hard to point to a single group that inhabited the archipelago but there were relatively large groups like Celts (descendants of Gauls) and Picts, etc. before the Romans.
It is not hard anymore. The British are compiling fascinating Genome maps of their people sampling tens of thousands. They can tell who was where first by measuring the occurances of indicator mutations and comparing them to surrounding populations outside of the UK.
The Irish (which includes the Scots) settled Ireland soon after the glaciers receded but they stayed there until quite recently. The North Welsh are thought to have been there for around 12,000 years ago as did the Cornish. The southern Welsh population is a little less ancient and, amazingly, are not related to the North Welsh. Who and what the Picts were is not certain but they were likely ancient Britons and are included in the Welsh population ... Pict just refers to pictures as it is a Latin term. There must have been a lot of tatoo parlours, up there.
What is really bizarre about the British findings is how very little people moved about. There are little genetic lines that have stayed put in their little counties good manty thousands of years. Cornwall and Devon are bordering counties with populations that have been there maybe ten thousand years, yet they are genetically distinct from each other. There isn't even a fuzzy area along the county border. They married their own, only their own and stayed away from those foreigners over in the next valley.
http://www.nature.com/news/uk-mapped-out-by-genetic-ancestry-1.17136