Eleven episodes of Doctor Who were filmed between October 30, 2017 and August 3, 2018.
In a press conference before the Doctor Who panel and San Diego Comic-Con, showrunner Chris Chibnall had this to say with two weeks of Series 11 filming remaining:
“We seem to be filming 11 episodes, and it’s only a series of 10.”
“I would definitely think there’s another episode after the end of the series, yeah.”
The filming for Doctor Who Series 11 was divided into five filming blocks of two episodes each. Jamie Childs directed the first filming block, consisting of The Woman Who Fell to Earth and another unnamed episode. Mark Tonderai directed the second filming block, consisting of The Ghost Monument and Rosa, Sallie Aprahamian directed the third filming block, consisting of Arachnids in the UK and The Witchfinders. Jennifer Perrott directed the fourth filming block, consisting of The Tsuranga Conundrum and another unnamed episode. Jamie Childs directed the fifth filming block, consisting of Demons of the Punjab and the unnamed Episode 10, the Series 11 finale.
That makes ten episodes. Who directed the eleventh? Wayne Yip.
— Ruther (@Ruther2) July 4, 2018
You will notice that the editor for the eleventh episode calls it the Doctor Who Christmas Special.
Wayne Yip also calls it the Doctor Who Christmas Special 2018 and Season Eleven’s Christmas Special on his online CV.
As for a guest cast list, so far we have Daniel Adegboyega in an episode of Doctor Who directed by Wayne Yip. Adegboyega’s CV lists him as playing a character called Isaac Sinclair. Isaac is likely Ryan Sinclair’s father, the one Ryan spoke of at his grandmother Grace’s funeral in The Woman Who Fell to Earth, when he expressed dismay that his father would not come to his own mother’s funeral.
— Ruther (@Ruther2) October 26, 2018
This sixth filming block, directed by Wayne Yip, was filmed concurrently with the fifth filming block in a practice called double-banking. Some filming with snow and pine trees occurred during this last filming period on July 12 at on Newton Beach in Porthcawl. It’s impossible to say whether the filming in Porthcawl was for a Christmas (or holiday) special but the presence of snow makes it likely.
One of the actors on location.
Wales Online briefly covered the filming and shared a video.
One more Facebook post shows the filming of a monolith with strange markings, an unusual tent and another actor.
As for when this eleventh episode airs, it was previously assumed it would air on Christmas day. However, it is also possible it will air on New Year’s day as a 2019 holiday special.
On November 1, The Mirror reported that Episode 11 will air on New Year’s Day.
“Doctor Who will not have a Christmas Day outing this year for the first time since the reboot in 2005.
Instead, 13th Time Lord Jodie Whittaker will have an hour-long special which runs at New Year – with a storyline that relates to the arrival of 2019.”
This is not an official announcement by any means and we will keep you posted on any new developments.