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When the pair met she had been working in the corporation's contracts office in the city.
He was also linked to Kylie Minogue after the pop star appeared in Doctor Who's Christmas special, in which they passionately kissed.
Last October, Tennant parted ways with actress Sophia Myles after a two-year relationship, following her move to Hollywood.
They, too, met on set - when Miss Myles played Madame de Pompadour in a 2006 Dr Who episode.
Miss Moffett played the Time Lord's child Jenny in episode six of the most recent series entitled The Doctor's Daughter and while it was a one-off appearance, the opportunity for her to return in later shows has been left open.
The actress, who has a six-year-old son named Tyler from a previous relationship, revealed after first meeting Tennant: 'David is dishy, isn't he?
'He's not only a good-looking but he is such a lovely, sweet guy.' Mr Tennant has been nursing his personal heartache after his mother Helen died after a five-year battle with cancer last summer.