We found out more on Breakfast this morning, when Billie Piper joined us live in the studio.
Tennant and Billie Piper, who played his on-screen companion Rose Tyler, are among those who will guest star.
Billie Piper is to make her debut at the National Theatre in a new play by Enron playwright Lucy Prebble.
The Effect, which stars former Doctor Who actress Billie Piper, is Prebble's follow-up to her hit 2009 play Enron.
James D'Arcy, who starred in ITV2 opposite Billie Piper in Secret Diary of a Call Girl, has been cast as Edward VIII.
Now, after giving up her role as Doctor Who's assistant Rose, Billie Piper's career is taking another turn - towards the West End stage.
Smith's TV debut was in the 2006 adaptation of Philip Pullman's The Ruby in the Smoke, which starred former Doctor Who companion Billie Piper as Sally Lockhart.
The leak involved one 45-minute episode called Rose, which is the name of the Doctor's assistant played by pop singer Billie Piper (pictured with the Doctor, Christopher Eccleston).
They are also offering odds on Sherlock star Martin Freeman, on Skyfall's Ben Whishaw and on former assistant Billie Piper returning to the series as the Doctor's new incarnation.
Also at the National, Lucy Prebble follows up her 2009 hit Enron with The Effect - a new work about love and neuroscience starring former Doctor Who actress Billie Piper.
Billie Piper is nominated for her role in clinical drugs trial drama The Effect, while the best actress category is completed by Hattie Morahan for A Doll's House and Kristin Scott Thomas for Old Times.
The most hotly contested category at the 2013 awards was for best actress in a play, where just 0.9% of the public vote separated winner Sheridan Smith (Hedda Gabler) from runner-up Billie Piper (The Effect).
BBC: Sheridan Smith and Rupert Everett shine at theatre awards
However, one-in-five of the people (22%) who took part in the poll also thought the transatlantic couple were the most mismatched, although the top award in this category went to media millionaire Chris Evans and his teenage bride, pop singer, Billie Piper.
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