The Queen was never a Princess of Greece & Denmark. Philip naturalized to British citizenship as Lt. Philip Mountbatten, RN prior to the marriage. Even if he hadn't, as a British princess who was heiress presumptive, she would never have used Philip's foreign title as her style because she took precedence in her own right.
Technically speaking, HRH The Prince Philip was not required to become a naturalized British subject before his marriage.. he was already British, according to the laws of nationality at the time.
His mother Alice, Princess Andrew of Greece and Denmark, was born in England at Windsor Castle.. in the presence of her great grandmother, Queen Victoria.
His grandfather, Prince Louis of Battenberg, joined the Royal Navy on 3 October 1868, thereby becoming a naturalized British citizen. He married Princess Victoria of Hesse and By Rhine in 1884.. and she was also born at Windsor Castle in the presence of her grandmother, Queen Victoria.
According to nationality laws of the time, natural-born subjects were those who were born within the dominion of the crown, as is the case with both Princess Victoria and Princess Alice, Philip's mother and grandmother.
Naturalized subjects were those who gave their allegiance to the crown, as is the case of his grandfather, Prince Louis of Battenberg.
Philip, however, was born in Greece and this may have negated his British citizenship, since women who married foreign men automatically lost their British citizenship.. although I am not entirely sure that would apply to members of the royal family. Regardless of this, the Sophia Naturalization Act of 1705 was still in effect.
This act granted English nationality to the Electress Sophia of Hanover, allowing all her future descendants a claim to English nationality. In 1957, Prince Ernest Augustus of Hanover successfully claimed citizenship of the UK & Colonies under this Act.
Although the Act was repealed from 1 January 1949, by the British Nationality Act 1948, some descendants can still claim citizenship based on their parent's rights under the law as it existed prior to 1949. And this obviously did not affect Prince Philip, since he married the Queen in 1947.
In fact,
Philip served in the Royal Navy during World War II, which could not have been possible had he not already been considered a British subject. His formal renunciation of his royal titles did not take place until 1946-1947, when he also took the surname Mountbatten. Prior to this date, Philip had no surname as a prince of the Greek royal house.
I believe that Parliament may have been ambiguous regarding his status, and with anti-German feelings after the war, the government thought it best for him to renounce his royal rights before he married Elizabeth... especially in light of his sisters' marriages to German princes with Nazi ties.
Had the situation been clearer at the time, it very well
could have been a marriage between HH Prince Philip of Greece and Denmark and HRH The Princess Elizabeth.
I have no doubt that had he married Elizabeth as a Prince, then her title would have been
HRH The Princess Elizabeth, Duchess of Edinburgh, Princess of Greece and Denmark.
Regardless of her precedence over Philip, the title
"Princess of Greece and Denmark" would have been included in her style upon marriage,
if Philip still held that title.. As heiress presumptive, she had no individual title of her own and would therefore assume the equivalent title of her husband..
which she did.. being styled Duchess of Edinburgh from 20 November 1947 to 6 February 1952.