In Doctor Who Series 9, episodes 3 & 4: Under the Lake & Before the Flood, are Cass and Lunn actually speaking sign language? (If the term speak is good enough for the Doctor, it's good enough for me too)
The British Deaf Association has publicly praised the episode, specifically calling out Cass' use of British Sign Language:
What was most heartening was that the Deafness of Sophie’s character, Cass, is incidental to the plot. She is an integral member of the group and was no different in any way, other than that she is Deaf and uses British Sign Language (BSL). Here at the British Deaf Association, we firmly believe Deaf people can do anything but hear and it’s encouraging for such a popular TV series to be cementing this view in its programme.
...But with enhancement
In Doctor Who Extra, Sophie Stone (Cass) and Zaqi Ismail (Lunn) talk about their characters a bit; in addition to revealing that Ismail had some prior experience with signing, they mention that they had to invent a couple of new signs:
Ismail: My elder sister's deaf, so it's been very exciting just to kind of...pick up my ability while I've been here, you know? Signing constantly. I'm excited for my sister to see this, if I'm being honest.
Stone: The things that we've invented? Yeah, yeah, we've got "Vector Petroleum", and the sign on Vector Petroleum looks like a little fire, and so we've come up with that [makes a sign, presumably meaning "Vector Petroleum"]. "Prototype", there's no sign for "prototype", so it's... [she gestures at Ismail, who demonstrates]. There are lots of different moments like that, aren't there?
It's worth noting that Sophie Leigh Stone is actually deaf. According to the Radio Times, she was the first deaf person to study at the Royal Academy of Dramatic Arts.
Yes, but with their own additions.
Sophie Stone (who plays Cass) is actually deaf, and Zaqi Ismail (who plays Lunn) has a sister who's deaf, so they're both well-versed in sign language. However, they did have to invent some of their own words in sign language to use in this episode, e.g. for "Vector Petroleum" and "prototype".
See this article, based on the following interview with the pair in Doctor Who Confidential:
In the video, Ismail also explains that his oldest sister is also deaf, which gave him a reference in working with sign language during the episode: his character often acts as Cass' interpreter.
"I'm excited for my sister to see this," Ismail says.
Finally, both actors talk about signs they had to invent in sign language for certain words that appear during the episode. For example, they didn't have a word for the corporation that Cass and Lunn work for, Vector Petroleum, so they came up with a sign that represented the corporation's logo. There also is not a current word in sign language for "prototype," so the two actors created their own.