Have you not noticed that that is a highly contentious issue, with many Scots and Welsh wanting independence?
The matter is different in Northern Ireland where the majority of the population want to remain part of the United Kingdom of Great Britain and Northern Ireland, with the rest generally wanting Ulster re-united with Eire.
The more enthusiastic Scots Nationalists used to waffle about " an independent Scotland within the EU" - the membership referendum results in Scotland favoured the UK staying in the EU; but there is no guarantee that an independent Scotland would be able to join it, or would not end up as nett contributors (as the UK was). You don't hear that call so much now, perhaps as a reaction to the awful mess in Northern Ireland thanks to the UK's and EU's mutual nightmare of geography hitting the EU's tangled protectionist regulations. In any case, I've wondered if they eventually spotted the irony in that slogan!
Whether those nations could thrive alone is another matter. I don't think they have thought through all the implications, particularly funding in entirety all their public services, transport systems, etc; forming their own currencies, tax, vehicle and driver licensing, welfare, etc. regimes, and joining or signing-to in their name, the ninety or so international bodies and treaties in which the UK is involved.
Many Welsh and Scots do want to stay within the United Kingdom but there are nearly as many Scots who want independence. I don't know the ratio in Wales.
As far as I know there are no Northern Irish wanting that, but a sizeable minority do want Eire and Ulster to be one country - Eire - governed from Dublin, not Belfast.
