Fallet a quirky short detective series.
Derry Girls is cute and entertaining.
Misfits young punks with superpowers is a tired plot, but somehow the writing makes this better than it should be. Endure the pilot, it improves.
If the OP enjoyed Sherlock, I recommend Prey.
The first couple of years were a fascinating police procedural. I don’t know how well they dated. When the writers ran out of things to say, and left, the producers change the show into a soapy.
If the OP likes Poriot, then Marple is the obvious next choice.
Roald Dahl’s Tales of the Unexpected is a classic anthology series comparable to Alfred Hitchcock Presents. Many episodes are on YouTube.
Speaking of classic series, you have to watch I, Claudius. Derek Jacoby, Brian Blessed, Sean Philips, George Baker, John Hurt, Patrick Stewart, et al. at the height of their careers.
They’re older shows, but before he did Sherlock, the same showrunner did Jekyll - a different modern retelling. It kind of goes off the rails and it features the worst American accent I’ve ever heard, but it’s definitely interesting.
He also did a very good comedy called Coupling - it gets compared to Friends a lot. (I like both shows, they are not the same at all).
For much more recent things, Catastrophe & Fleabag (both comedies).
I think Peep Show is the best show ever made, only just slightly better than Father Ted, but the humour may not appeal and there’s no point forcing it.
More broadly appealing would be Hamish Macbeth, a very wry Scottish-based police show. Very much in the same vein as Doc Martin with quirky locals, and starring the ever-excellent Robert Carlyle. Not sure if its ever been streamed, but probably exists as a DVD box set going for tuppence these days.
Siân Phillips
This.
Though I agree also you’ll decide if it’s for you or not very quickly.
What is it with British seasons?
New Tricks ran 15 season but only 90 episodes.
They believe in quality over quantity and don’t flog shows long after their prime. The seasons (“series”) are deliberately kept short for the same reason.
John Cleese was offered the opportunity to make more episodes of Fawlty Towers, but he turned it down. He thought Basil had already run his course.
The Criminal series on Netflix was pretty good, and the UK series was the only one to get a second season.
Marcella, also on Netflix, was good as well. It’s quite dark, and a slow burn kind of show.
Yesssssssss. Although I’d place Spaced second, not Father Ted (but FT is up there!)
If you like Foyle’s War, you’ll also enjoy Danger: UXB. It’s the story of the Royal Engineers’ bomb disposal units during WWII, starring a young Anthony Andrews. Every episode has at least one butt-clenching moment as you wait to see who’s going to get blown to bits this time.
The Jewel in the Crown is the story of the last days of the British Raj in India. A couple of years ago, it was shown on PBS for the first time in several decades, and it was just as good as I remembered.
lol well why watch marple when you can have one of the best british actresses ever ripping off christie in murder she wrote ? 
<runs for cover)
Actually, they just mentioned 8 out of 10 Cats, which is a different (related) show.
So’s Countdown.
Another great quiz show is Only Connect, presented by Victoria Coren-Mitchell. It’s excellent.
And I think Netflix’s Sex Education needs a shout-out.
Also, seconding Misfits.
And That Mitchell & Webb Look is also great.
Rumpole of the Bailey - 7 seasons and 42 episodes broadcast between 1975 and 1992.
If you liked Death in Paradise, you might like Father Brown, a priest who solves murders in a small Cotswolds village. There are a lot of murders. Seriously, don’t ever visit Kembleford.
Downton Abbey is a classic, even if it is just a pulp soap opera at heart.
Depending on your age or maybe political slant, you might try The Young Ones, about 4 students living together, very 80s, very anarchic humor.
Doc Martin has been mentioned but it has to be mentioned again.
If you’re a fan of cringe humor, there’s Ricky Gervais’ original UK version of The Office. In the same vein but even better than The Office imho is his show Extras, about movie extras. It’s worth it just to hear Patrick Stewart pitch his brilliant screenplay idea.
Also, if you like an anthology style show with discrete stories you can’t get much better than Inside No. 9, from 2/4 of the League of Gentlemen [another recommendation itself]. These are standalone twist-in-the tail creepy-comedy-dramas, and are generally excellently constructed and got a lot of stalwarts of British theatre and TV involved.
Also two other detective shows -
River
Unforgotten
Nicola Walker is the common factor in these, and anything with her in it is doubleplus good.
I’ll pile on in agreement with this; Peep Show portrays a quintessentially English desperation beautifully, and is outright hilarious. The more recent Mitchell and Webb series ‘Back’ is worth a look too. Great supporting characters, great script, and a fantastic cameo from Anthony Head.
I think the British versions of Who Wants to Be a Millionaire? and The Weakest Link were vastly superior to the American ones. Much less idle chatter and much sharper contestants (most of the ones I’ve seen, anyway).
Is Mastermind still on in the UK? Quiz shows don’t get any more intense than this!
Speaking of WWtBaM?, watch the full version of the BBC documentary Major Fraud on YouTube if you haven’t already. See how easy it is to con a quiz show out of lots of money, so long as you don’t get too greedy!