Been a while since I checked it, but a group of teams from Wales stopped playing in competitions organised by the Welsh FA and started to play in competitions organised by the English FA. Off the top of my head, the teams that did this are:
Might be a couple more, but these teams were called the Exiles as they stopped playing in Welsh competitions
A few decades later, these clubs continued to play in English competitions, but made up with the Welsh FA, and were invited back to play in the a cup. I think there's a cup called the Premier Cup (or there was) which Wrexham Swansea and Cardiff won for a good few decades on the bounce as they were so much better than the likes of TNS!
Hope that helps!