Yes, Philip of Spain was King Regnant of England.
Under the terms of the marriage treaty, Philip was to enjoy Mary I's titles and honours for as long as their marriage should last. Their joint royal style (after Philip ascended the Spanish throne in 1556) was: Philip and Mary, by the Grace of God King and Queen of England, Spain, France, Jerusalem, both the Sicilies and Ireland, Defenders of the Faith, Archdukes of Austria, Dukes of Burgundy, Milan and Brabant, Counts of Habsburg, Flanders and Tirol.
Acts which made it high treason to deny Philip's royal authority were passed in Ireland and England. The Privy Council instructed that Philip and Mary should be joint signatories of royal documents, and this was enacted by an Act of Parliament. As the new King of England could not read English, it was ordered that a note of all matters of state should be made in Latin or Spanish. Philip and Mary appeared on coins together, with a single crown suspended between them as a symbol of joint reign. The Great Seal shows Philip and Mary seated on thrones, holding the crown together. The coat of arms of England was impaled with Philip's to denote their joint reign. All official documents, including Acts of Parliament, were to be dated with both their names, and Parliament was to be called under the joint authority of the couple.
The numeral of the next British Monarch ascending to the Throne under the name “Philip” is debatable; both Philip I and Philip II are possible. Although Philip of Spain (Queen Mary I’s husband) was King Regnant of England and Ireland, it was only for the duration of their marriage, so he’s often not mentioned in the list of 'proper' Monarchs (the ones which usually omit Empress Matilda and Jane Grey as well).
The reason why the next “King Philip” may chose to be known as “Philip I”, rather than “Philip II”, is that Philip is not exactly a very popular figure in English/British history. The wars he wages against France (and which England supported, although a special clause in the terms of the marriage treaty stipulated that Mary wasting obliged to support Philip's wars) cost England its last bastion on the mainland – the port Calais. And of course, it was Philip who sent the Spanish Armada to invade England during the reign of Elizabeth I.