July 1403, battle of Shrewsbury. Owain Glyndwr's forces link up with Percy's Northumbrians in time to inflict a crushing defeat on the royal army. Henry IV and the Prince of Wales (the future Henry V) are both killed. The most senior surviving son of Henry is the 16 year old Duke of Clarence who is apparently in Ireland at this point and fairly helpless to do much when Owain and Hotspur declare his family to be usurpers (which they are) and recognise Edmund Mortimer, the heir presumptive of Richard II, as the rightful king. As Mortimer is only 12 years old a prisoner, his uncle, also called Edmund - and a prisoner of Glyndwr - is declared regent.
Mortimer is being held in Berkhamstead Castle in Herefordshire by a Lancaster loyalist, Sir Hugh Waterton. Waterton will probably want to get Edmund as far away from Glyndwr and Percy as possible (Shrewsbury is only a couple of day's hard riding north at this point) but he has the problem that the commander of Lancastrian forces in Herefordshire at this point is Richard of Conisburgh, 3rd Earl of Cambridge who is not a loyalist - he's the son of the Duke of York and the one who the Yorkist claim to the crown was transmitted through for the Wars of the Roses and may well by this point be mulling over the possibility of making a grab for the throne himself.
So we have three claimants to the throne - one a prisoner (and his regent and likely replacement if he gets shot trying to escape is a Welsh puppet), one in Ireland and one a nonentity. England collapses into the Wars of the Roses fifty years early and spends most of the 15th century tearing itself apart. Glyndwr uses the opportunity to consolidate his position in Wales (purging the marcher lords, basically) and calls a parliament and issues his own legal code. He basically sits out the war in England, maybe intervening occasionally if someone looks like winning, and passes on an independent Wales to his son, probably one that's somewhat
larger.
That would get you to about 1500 or so, but to get to 1800 you probably need the war to break England up completely so none of the bits are strong enough to take down Owain's state - a final solution to the wars that ends up with England looking more like the Holy Roman Empire, with the king directly ruling only a small area around London, perhaps?