Since 2005 there has been a Doctor Who Christmas Special every year, although it's worth remembering that strictly speaking "The Christmas Invasion" was actually the 2nd (1965's "The Feast of Steven" was technically the 1st!). These traditionally perform far better than the ordinary yearly season of 13 shows (and in the case of "Voyage of the Damned" and "The Next Doctor" phenomenally better).
The Christmas specials are heavily trailed in the preceding weeks, so the audience has a far better expectation of whether they might like it or not. This is probably the reason behind the larger difference in ratings across the years, when compared to the relatively stable audience for the ordinary series. Since no audience drops below 9 million, it's a fair bet that the core audience is still there, but additional viewers are probably enticed in by certain guest stars or interesting concepts. Kylie Minogue was probably the draw for the 13 million that tuned in for "Voyage", while the intriguing idea that "The Next Doctor" might actually feature the next Doctor (it didn't) probably helped to boost the ratings that year.
Then of course there's the draw of an actual New Doctor. So far there's been two Christmas specials with a regeneration - 2010's "The End of Time Pt 2" and 2014's "The Time of the Doctor". David Tennant's January 2010 swan song achieved the 4th highest ratings of any Christmas special whereas Matt Smith's farewell was 6th.
Fan opinion (and to a certain extent the Media) would have us believe that the now perennial Doctor Who Christmas Special is no longer as good as it was in the heady days of David Tennant. However we can plainly see above that up until "Voyage of the Damned" viewers failed to reach 10 million, whereas almost every special since then has been watched by over 2 million more. Even Matt Smith's 2012 and 2013 outings, although appearing to suffer a drop, still comfortably reached 10.5 million. But what about 2015 and the new Doctor?
There are two things to take note of here. Firstly the smallest Overnight figure for a Doctor Who Christmas Special ever - 6.34 Million. Secondly a Timeshift of just under 2 Million. This equates to a Final viewing figure of 8.28 Million, the lowest Final figure ever. Is this a disaster? Or is there something else going on here?
Well for the first year the L+7 figures are freely available, and they show that Series 8 of Doctor Who saw an increase of between 10 and 14 percent of viewers through non-TV means - mainly IPlayer, and the figures for the Christmas Special of 2015 also show a similar increase of about 1.5 million. Although this doesn't make it the worst-performing Christmas Special (that would be "The Runaway Bride" in 2006), it does make it the second worst.
However by 2015's "The Husbands of River Song" things look a bit different. 5.77 million Overnights shows that it was watched by the least viewers on the night for any Doctor Who Special. 2016's "The Return of Doctor Mysterio" appears to fare no better at 5.68 million. But hang on. Let's just take a look at the Audience Share.
"Husbands" was watched by 29.4% of the total viewing audience for that night (19.6 million), while "Mysterio" was watched by 27.1% of 20.9 million. OK, admittedly the 2008 Christmas Special "The Next Doctor" managed to nab 50.5% of the an entire audience of 23 million, but still Capaldi's Christmas jaunts didn't do badly at all. In fact if you look at the Series 10 page you'll see that it's much the same story for the regular series - between a quarter and a third of TV viewers still watch Doctor Who, even at Christmas. This is still a success in TV terms.
-Spacewarp July 2017