In terms of horror, there was the "torture porn" sub genre starting out. A lot of them are really entertaining. Imho they take their influences from Old-School Horror films like Texas Chainsaw Massacre and Teenie Horror films from the 90s and add lots of cruelty and visible violence.
Hostel 1 + 2
Saw 1-3
Wolf Creek
High Tension
are some that I really enjoyed. There are quite a few bad ones too.
Then you have Rob Zombie who's doing his own weird genre.
Sam Raimi made a remake of his old Evil Dead films, Drag me to Hell is nice too.
There's a new crop of Zombie films with 28 Days / Weeks later being quite influental. The Dawn of the Dead remake is alright too, George Romero's recent films too. You'll also find comedies/parodies on these films, the two best ones of them British (Severance, Shaun of the Dead).
Cabin in the Woods is a more fun spin at the modern Horror genre.
The Mist isn't liked by everyone, but to me the best regular Steven King adaptation.
There are smaller, brutal ones too like A l'Interieur or The.
Poughkeepsie Tapes. Or takes on the genre by master directors like Lars von Trier (Antichrist). Or the not-so-Horror but still Vampire themed Only Lovers left alive.
Speaking of Vampire films, there were a lot of average Action themed films, can't recommend any of them. Maybe Daybreakers.
The best big monster movie ever made is The Host from around 2006.
Big Hollywoods contribution is JJ. Abrams Cloverfield and the "smaller" 10 Cloverfield lane, where the first one adds an interesting way to present the plot.
Adding to that, there's some great stuff on TV too.
True Bloods first few seasons are amazing.
Then you have a number of average TV shows and movies that are liked by a lot of people, but imho more aimed at teenagers like The Walking Dead or Twilight.
Original CSI had some great Serial Killer plots. Some connected episodes spun quite well done stories, I would consider those more in the Horror domain than the usual mystery episodes.
Probably not heard of these but this one kind of grew on me bit surreal but fun!
The Cottage
Also if you like TV series in same kind of quality scripting acting as Breaking Bad, Game of Thrones and liked The Thing then this TV series will keep you hooked. Just watch all the seasons on a rainy day will keep you curious and loved it!
Sadly George A. Romero passed away this evening. Speaking of horror, I suggest the rewatch of Night, Dawn and Day of the Dead, real cults with an actual social content.
"When there's no more room in hell, the dead will walk the earth"
Not so much a horror but more so a thriller, all the while belonging to the Italian horror genre giallo—I suggest watching Tenebrae by Dario Argento.
If you like it then I also suggest watching other gialli films by Dario Argento, Mario Bava, Sergio Martino, and Lucio Fulci. There are probably more out there. Giallo is a very fun, over the top horror genre that spawned in Italy when importing foreign literature of the same genre was banned, and as a result it's got this really enjoyable pulp style to it: sexy, spicy, and sometimes scary. It's definitely hit and miss.
scream
scream 3
the exorcist
se7en
saw
saw 2
28 days later
alien
aliens
silence of the lambs is one of my favourite films but that's a thriller.
edit - also, add 'don't look now' with donald sutherland and julie christie. it's not scary (apart from the shit-thyself moment at the end) but it's a classic in the horror hall-of-fame and a good movie to help appreciate the subtleties of a movie and how that can make it scary in it's own right.
no idea if you've seen any/all of those but they're the movies that come to my mind.
comedy:
peep show is a good shout by abso above, although I haven't seen past series 5.
arrested development looks pretty funny but i haven't watched it yet (edit - although that's not british)