Dr Who gets labelled as SF, but it's really Victorian horror in the tradition of Wilkie Collins and Henry James, with a coat of silver science fiction paint and more than a few nods to Shakespeare. It's always had that terrifying aspect with its focus on ghosts, wizard, witches, and monsters, some of whom happen to be alien, all of whom are still recognisable as distorted humanity.
For more mainstream alien SF horror you want Nigel Kneale's Quatermass series. If you squint hard you can see the influence of the original 1950s Quatermass episodes in Dr Who's DNA.
IIRC one of the original aims of the series was to teach children about important historical events by wrapping them up in a Sci-Fi-time-travel-gothic-horror story. Which is then particularly ironic given that the original airing was postponed due to the Kennedy assassination. I particularly loved the story where the Doctor accidentally started the Great Fire of London, for example, and people have hailed the Marco Polo story as an example but I was too young and/or not yet born when that came out… sorry I’m not going to go and fact check any of the above claims right now, unfortunately as a grown up I have to resist the temptation to fall into an enormous nostalgia hole in favour of doing some actual work. (I’m sure the internet won’t hesitate to correct me if I’m wrong)
The Quatermass tip is a good one, I’ve heard good things but never actually checked it out yet. Personally I stopped liking horror very young and preferred the Space Opera direction, particularly when Terry Nation (creator of the Daleks) went off to make Blake’s 7 for the BBC instead. High concept: Shakespearean actors from RADA and/or the RSC do a low-budget, ludicrously camp rebels-against-the-evil-empire tale while somehow pretending it’s serious drama (which it occasionally was) and keeping a straight face all the way through. Not to mention what weird effects the evil androgynous boss-lady Servilan had on my just-developing sexuality (I confirmed this with friends of the same age, it’s not just me…)
For more mainstream alien SF horror you want Nigel Kneale's Quatermass series. If you squint hard you can see the influence of the original 1950s Quatermass episodes in Dr Who's DNA.