Cult
Rex Features
The Scottish actor was spotted leaving his home with 23-year-old Moffett, who plays his on-screen daughter on the cult BBC show, over the weekend.
A friend of Moffett said: "They have been going out together for a while now but meet up at each other's house so as to avoid being spotted by Who fans.
"David can't go anywhere without attracting attention and it's early days so they don't want any distractions or fuss made about what's going on.
"It started with some friendly dinner dates but has progressed quickly and they are now in a serious physical relationship.
"Even with his busy schedule, David is making a lot of time to spend with her, so he must really like her."
Moffett is the daughter of former Doctor Who star Peter Davison.
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