The next day in Parliament the House of Commons proposed that a bill be prepared to remember that occasion:
Anniversary of the Restoration.
Resolved, That a Bill be prepared for keeping of a perpetual Anniversary, for a Day of Thanksgiving to God, for the great Blessing and Mercy he hath been graciously pleased to vouchsafe to the People of these Kingdoms, after their manifold and grievous Sufferings, in the Restoration of his Majesty, with Safety, to his People and Kingdoms: And that the Nine-and-twentieth Day of May, in every Year, being the Birth Day of his Sacred Majesty, and the Day of his Majesty's Return to his Parliament, be yearly set apart for that Purpose.
Ordered, That Mr. Pryn, Mr. John Stephens, Serj. Maynard, Mr. Finch, Mr. Skipwith, Mr. Charleton, Mr. Turner, and Serj. Glyn, be the Committee to prepare the said Bill.
Restoration Day was also called Oak Apple Day. This website explains why:
Boscobel House was on the site of the former Augustinian House of the White Ladies dedicated to St. Leonard of Limousin, dissolved in 1538. The Giffard family, in whose oak tree Charles hid, were a recusant family, thus the priest-hole in their house.
In spite of the fact that Charles had been aided by Catholics and had escaped capture by hiding in a priest-hole, he had promised to uphold the Church of England, and so among the other efforts in Parliament on May 29 and 30, the House of Commons proposed bills against Catholics. On the 29th:
Col. King reports a Proclamation against Jesuits, Seminaries, and Popish Recusants; which was read the First and Second time; and, upon the Question, agreed unto, to be the Form of a Proclamation, to be presented to the King's Majesty.
Ordered, That the Lords Concurrence be desired to this Proclamation.
Col. King to carry it to the Lords.
On the 30th:
Col. King brings Answer from the Lords, that, as to the Proclamation against Papists, which, by Command of the House, he had carried this Day to the Lords, the Lords will return Answer by Messengers of their own.
Seventeen years after the Restoration, Charles wasn't even able to save Blessed John Gavan, SJ, who had taken his final vows as a Jesuit in front of the Royal Oak at Boscobel House--he did arrange for Gavan and his companions, victims of the Popish Plot, to be hanged until dead, on June 20, 1679.