As of 27 April 2024, Medlands' England, Kings 1066-1837 A. Kings of England 1154-1399 does not include a son "Philip" as son of Henry II.
Apparently, Cawley doesn't accept the quote with source citation below as a primary or secondary source.
------------------------------------------------------------------------------------------------

From “History of Great Britaine Under the Conquests of Romans, Saxons, Danes, and Normans” (London, 1611) By John Speed.

(106) Philip, the fifth sonne of King Henrie, and Queene Eleanor, may bee mistrusted, to be mistaken by Antiquaries of our time, as misunder-standing the ancient writers, who mentioning the birth of Philip the Kings sonne, might by good likelihood, be thought to meane, Philip sonne of Lew•… the Yonger King of France, who was borne about this time, and was after King of the same Countrey. But Mr Tho∣•…as Talbot, an exact trauailer in genealogies, hath not onely set him downe in this place, amongst the children of this King, but also warranteth the same, to bee done with good authoritie: howsoeuer, it is apparant, his life was verie short.

References

• The history of Great Britaine under the conquests of ye Romans, Saxons, Danes and Normans Their originals, manners, warres, coines & seales: with ye successions, lives, acts & issues of the English monarchs from Iulius Cæsar, to our most gracious soueraigne King Iames. by Iohn Speed. Speed, John, 1552?-1629., Schweitzer, Christoph, wood-engraver. book 9 HENRIE THE SECOND, DVKE OF NORMANDY, GVYEN AND AQVI∣TAINE, THE FORTIE THIRD MONARCH OF THE ENGLISH-MEN; HIS RAIGNE, ACTS AND ISSVE. CHAPTER VI.*. [Monarch 43.]*. [Henry second] link