Parliament wasn't really powerful until the 17c, though. The medieval institution was consultative, and its power gradually eroded as the monarchy became more stable. In the 15c, England was solidly absolutist - the Wars of the Roses have to be understood as a conflict between two factions fighting for absolute control, and individual nobles could decide who to side with, but Parliament overall wasn't much of a factor. In the 16c, it was even more absolutist. Parliament only became relevant once Britain got a weak king in Charles I, who was too sympathetic to a despised religious minority to boot.
What really happened in the 17c is that the monarch pissed off too many powerful magnates at once, and moreover the powerful magnates were a commercial class and not merely a nobility as under Henry VI. Once we shift from the traditional (and wrong) story of Parliament slowly evolving into a powerful legislature to a story in which Parliament acquired power through revolution against Charles I, mirroring revolutions in the Netherlands and Switzerland (both against the Habsburgs), the question of what happened in the Middle Ages becomes moot.
In other words, a TL in which Parliament was never formed in the 13c couldn't really affect future political development, except through distant butterflies. If the centuries of monarchical feuding end up producing a strong commercial class, then eventually this commercial class would rebel and establish something like a republic, as happened in OTL in 17c England, 18c France, the 16c Low Countries, 13c Switzerland, and the 14c Hanseatic League. If there's no strong commercial class, there's not going to be such a revolution. By the Early Modern Era, any such revolution is going to produce something like a parliament of its own; if there were no national parliament to use, it would have invented one.