Prince Philip is a deceitful philanderer who cheated on Queen Elizabeth on multiple occasions. In 1948, a photographer named Baron Nahum introduced Prince Philip to Patricia Kirkwood, a young showgirl. They met in Kirkwood’s dressing room at the London Hippodrome before Kirkwood’s performance. This meeting allegedly involved dinner and dancing all night, leaving Elizabeth at home alone and eight months pregnant.
After this meeting, Philip and Kirkwood met on at least seven more occasions. While Kirkwood continually denied any affair until her death, Philip never cleared her name. Since Prince Philip never denied the rumors, this makes it obvious that he lied about his relationship with Kirkwood.
Therefore, Prince Philip is a philanderer.
Furthermore, Prince Philip has involved himself in the lives of other women throughout his marriage to Queen Elizabeth. In 1957, the Baltimore Sun released a story that Prince Philip was allegedly involved in an illicit relationship with an unnamed woman.
Beyond these two affairs, the public accused Prince Philip of romantic connections to other performers like Helene Cordet, Merle Oberon, and Anna Massey. 
With the number of accusations related to Prince Philip’s connections to women, there is obviously some truth in the allegations. This means that Prince Philip was unfaithful to his marriage and engaged in some sort of philanderous relationship.