I'll join in to the history lecture with this offering...
In the years after the Romans deserted Britain, (Circa 450AD to 650AD) those who lived in the area we now call England were under attack constantly from Saxons and other tribes.... so they moved West to avoid being killed.
Because they were running from the onslaught, they were knowns as Welchers, or Welsh....so they upped sticks and moved into the area we now called Wales.
So really, (after the Celts) the origins of Welsh people are really rooted in the native English blood.
The Saxons became eventually conquered by Norsemen, and then the Normans..
Those who THEN occupied England, started to subdue the relatively new Welsh peoples.
So as Ian says, where do you draw the line date-wise?
I have 'fled' to Wales from England for two reasons,
1, I adore the Llandudno area and always have.
2, I could not stand how my own birthplace had been 'invaded'... so I too had to flee to the West.