The 2017 A Christmas Carol Goes Wrong was truly bad. It felt forced, and I do not think it was filmed before a live studio audience, I think it was either shown to an audience or canned laughter was added, as the audience did not play a part of the show, as it did during the brilliant Peter Pan Goes Wrong back in 2016.
You think wrong.
Both were done in front of a live studio audience. Peter Pan at Pinewood - Christmas Carol in Studio 1 at Dock10/Mediacity. Both recorded in the September before Christmas transmission.
For Peter Pan, it was recorded twice. Afternoon and evening on the same day, and (if it's out there) the audience were clearly shown several times. Not sure about Christmas Carol, may have been just the one recording session.
BBC Tickets did the audience wrangling. There was a live audience for both shows.
There may have been some 'enhancement' of the laughter for some gags that fell flat in recording, done in post-prod which would give the slightly 'canned' sound.
My user name might look like Hatton Cross, but it's pronounced Throatwobbler Mangrove.