Yes. King Edward III took part in more than 50 tournaments, sometimes incognito. His son and heir, the Black Prince, also jousted incognito, as did many knights during Edward III's reign.
The Annales Paulini (1307-41) mentions the Dartford jousts of 1331. In Edward III and the Triumph of England, Richard Barber says:
The knights were in uniform costumes of green tunics and mantles with
red hoods....To conceal the king's identity, they were all masked.
The easily accessible article Tournaments in the Fourteenth Century also mentions this.
Nigel Saul, in Chivalry in Medieval England, says:
In 1334 at a major tournament at Dunstable the king appeared under the
arms of the Arthurian knight Sir Lionel. On several later occasions he
appeared wearing the arms of members of his household entourage.
Participating incognito in the manner of Arthurian heroes was a way of
linking the fantasy world of romance to the practical world of
preparation for war.
Edward III appeared several times at tournaments as Sir Lionel, though, so presumably someone eventually figured out who 'Sir Lionel' was.
In A Short History of the Hundred Years War by Michael Prestwick, the author states that:
Edward III was a great patron of tournaments, in which he himself was
often an eager participant....often taking part incognito. There was a
playacting element, as when Edward and some knights dressed as the
Pope and some cardinals at a tournament held at Smithfield in 1343.
The chapter War, Plague and Chivalry (1346–54) from David Green's The Black Prince says that both Edward III and his heir fought incognito:
Meetings of the Garter were often accompanied by splendid tournaments,
many of which were staged in true Arthurian style with knights
fighting incognito or wearing fantastic costumes. Both Edward III
and the Black Prince are known to have participated wearing disguises
Saul also offers an explanation as to why jousters sometimes appeared incognito:
Remarkably perhaps, even the donning of disguises in tourneying served
a practical purpose. It made for equality between competitors by
ensuring that a lesser knight did not defer to the superior blood of
This question went unanswered for 3 months, and I'd given up looking myself. I came across this answer completely by chance but, perhaps with hindsight, Edward III is as obvious a candidate as anyone.
If anyone can find any other clear examples of kings or heirs jousting incognito, I'll accept that answer ahead of my own. For those interested, Richard II is an unlikely candidate (only one joust apparently), Henry V didn't like jousting (though this doesn't necessarily rule him out), while Edward I took part in many tournaments but doing it incognito doesn't seem to have been common then - still, maybe worth investigating. Also, this question is not restricted to English kings.