the date has been announced

Prince William of Wales and Miss Catherine Middleton will marry on April 29, 2011 at Westminster Abbey.

http://www.telegraph.co.uk/news/uknews/royal-wedding/8153299/Royal-wedding-Prince-William-to-marry-Kate-Middleton-on-Friday-April-29-2011.html

Princess Patricia of Connaught was the first member of the royal family to marry at Westminster Abbey since 1296 when Prince Edmund, son of Henry III, married Aveline de Forz.  Princess Pat, as she was known in the popular press, was the youngest child of the Duke of Connaught.  She married Captain Alexander Ramsay of Mar on February 27, 1919 in a ceremony at Westminster Abbey.
The princess, who renounced her royal titles when she married,  set a precedent for future royal marriages, at the Abbey. 

 * February 28, 1922:  Princess Mary, the only daughter of King George V and Queen Mary,and  Viscount  Lascelles (future Earl of Harewood)
*  April 26, 1923:  The Duke of York (George VI) and Lady Elizabeth Bowes-Lyon
*  November 29, 1934   The Duke of Kent and Princess Marina of Greece and Denmark
*  November 20, 1947  Princess Elizabeth and Lt. Philip Mountbatten
*  May 6, 1960   Princess Margaret and Mr. Antony Armstrong-Jones
*  April 34, 1963   Princess Alexandra of Kent and the Hon. Angus Ogilvy
*  November 14, 1973  Princess Anne and Mr. Mark Phillips
*  July 23, 1986   Duke of York and Miss Sarah Ferguson

On November 6, 1935, the Duke of  Gloucester married Lady Alice Montagu-Douglas-Scott at the Chapel at Buckingham Palace.  The wedding was scheduled to take place at Westminster Abbey, but the ceremony was moved to the palace following the death of Lady Alice's father, the Duke of Buccleuch. 
Princess Alice, Duchess of Gloucester, wrote in her memoirs:  "There was great consternation at his death, and much talk of the wedding being postponed; but since the King  seemed no less likely to die, it was decided to go ahead, in the private chapel at Buckingham Palace rather than the public splendour of the Abbey,  This suited the King very well, and I was only too glad not to have a grand wedding.  Immediate members of our families and close friends were the only guests, to the disappointment of members of the Diplomatic Corps and many hundreds of others."

Westminster Abbey is a royal peculiar, which comes under the the sovereign's jurisdiction, and not a Bishop. 
William will need his grandmother's permission to marry (according to the Royal Marriages Act).  He will also need her permission to marry at the Abbey.
In fact, marriages at the Abbey are limited to members of the Royal Family, members of the Order of Bath and their family, and those who live in the Abbey precincts.

Members of the Royal Family can marry in other  Royal Peculiars as well, which include St. George's Chapel, Windsor;  the Royal Chapel on the Windsor estate near the Royal Lodge;  the Chapel Royal and the Queen's Chapel  at St. James's Palace; the Chapel Royal at Hampton Court, and two chapels at the Tower of London.
Princess Alexandra, Duchess of Fife, and Prince Arthur of Connaught were married at the Chapel Royal, St. James's Palace, in 1913.
Princess Maud of Fife and Lord Carnegie were married at the Chapel, Wellington Barracks, in 1923.
The present Duke of Kent's marriage to Katharine Worsley took place at York Cathedral in 1961.
Prince and Princess Michael were married in a civil ceremony in Vienna in 1978.
Prince Edward and Sophie Rhys-Jones were married at St. George's Chapel, Windsor.