The act of assigning titles is very confusing but if you are writing an historical period piece, it's extremely important to know who is what. Let's begin!
ROYALTY
Of course, England is the seat of the monarchy and its highest title is King or Queen. At this time, Queen Elizabeth reigns supreme over England, Ireland, Wales and several other English commonwealths and territories, formally known as Queen Regnant. Her husband is formally known as Prince Consort Philip, but you usually only hear Prince Philip. Their formal last name is Mountbatten. When addressing the Queen or her consort, he or she is referred to as "Your Majesty."
After the King/Queen come the Prince and Princess. This would apply to Prince Charles and Princess Diana, now deceased. It also applies to others in line for the throne, Prince Andrew, Prince Edward and Princess Anne. Charles is known as the Prince of Wales, Andrew is known as the Duke of York, Edward is known as the Earl of Wessex and Anne is known as the Princess Royal. The Prince/Princess is formally referred to as "Your Highness". The Prince's children are called Prince, as in Prince William and Prince Harry but the children of a Princess are not automatically given those titles, though they may be granted by the monarch (King/Queen).
For further information, the first born son is granted the title of "Prince of Wales" and his wife is known as the "Princess of Wales". When they were still married, the formal title would be Charles, Prince of Wales, Diana, Princess of Wales and Princes William and Harry, Princes of Wales. The second born son is granted the title of "Duke of York" and the third born son is the "Earl of Wessex".
DUKE/DUCHESS
The next rank is Duke and Duchess and both as formally called "Your Grace". Close friends might call them "Duke" or "Duchess" but most were most likely known by the name of the title, example given: "The Duke of York, His Highness, Prince Andrew". Prince Andrew would never be known as Duke Mountbatten.