Prince Charles can only claim the title "Prince of Wales" in terms of the English Statute of Ruddhlan, 1284. This is not recognized under native Welsh law. The Welsh Principality of Gwynedd is arguably the most senior- the only Princes of a briefly united Principality of Wales were from this line, also known as the House of Aberffraw. The Welsh principalities could only pass through the male line with legitimate sons taking precedence over illegitimate sons. The last Welsh Prince Dafydd III was of an illegitimate line. The only serious claimants today are Evan Anwyl of Tywyn (I have actually spoken to him), and his son Daffyd, and two cousins, one Roger Anwyl, who is a professor at Trinity College in Dublin, Ireland, and the other Phillip Anwyl who lives in Sussex, England. Daffyd is married to Caroline Owen of Nantwich. They have a daughter, Carys Anne Anwyl, born in 2008. Daffyd and his family live in Birmingham, or Manchester. The Anwyl family claim descent in the male line from Rhodri II Ap Owain, Prince of Gwynedd 1170-90, uncle of Llewellyn II "the Great", Prince of All Wales 1216-1240, and Prince of Gwynedd from 1195. Llewellyn was the grandfather of Dafydd III, the last prince who was brutally executed by England's King Edward Plantagenet.
Recently, David Wolcott (see
www.ancientwalesstudies.org) has challenged the Anwyll family's descent, but Wolcott's arguments have not been independently supported, or verified, so Evan Anwyl's claim still stands. Ultimately, Y-DNA tests will resolve this debate.
Most Welsh respect the Queen, but the same respect does not necessarily extend to her son Charles. The native Welsh royals stand quite a good chance of being restored, if Wales broke away from England. The republican camp in Wales is small, even among Plaid Cymri.