Maybe if he pulled a few strings? 
Was that not just 17 episodes?
Yep, a very short run.
The Repair Shop.
How about Call the Midwife?
Vera. I love Vera. And Shetland, though it’s Scottish.
I hate Inspector Morse, I thought the character was horrible. But I really like Endeavour, and I especially like Lewis.
I forget. Which one was Call?
I am definitely hooked on Britbox & Acorn … especially police procedurals with a few exceptions…
I cannot recommend The Detectorists highly enough- well written, deceptively easy pace but just filled with layers of great writing, characters and details. MacKenzie Crook wrote & directed and acted lead- amazingly talented , I had no idea!
Ditto on Shetland- its dark and beautiful. Also really love Happy Valley (though I think in US you have to purchase through Prime now) - Sarah Lancashire is great.
Wallander is good- I’ve seen the Kenneth Branagh one and the Young Wallander series.
Grantchester
The Mallorca Files
The Pembrokeshire Murders
The Bay
The Coroner
Unforgotten
The Ruth Rendell Mysteries
The Inspector Lynley Mysteries (with the incomparable Sharon Small)
There’s a reason why your post and this one are the only posts to mention Father Brown. It’s professionally produced and sort of OK, but not worth recommending.
I will recommend it, especially the earlier seasons.
Re: Death In Paradise. I liked it when Ben Miller starred. I never really warmed up to Kris Marshall’s take on the part. It was good to see Danny John-Jules working.
Which reminds me of another great series: Red Dwarf.
There’s a great piece of investigative work into the origin of a Yes Prime Minister joke here (although if you are unfamiliar with British tabloids it might go over your head):
However the scene about manipulating opinion polls is the most genius moment:
Do you get Absolutely Fabulous (Ad Fab) - well worth a watch.
Last Tango in Halifax
Killing Eve
The Bodyguard
Peaky Blinders
I’ve been planning to start this thread for a while now. I have watched so many I’m running out. The best of the best are The Bay, Dr. Foster, Keeping Faith, and the very very best of them all is Foyle’s War. The best high-action cop show is Line of Duty.
I’m forgetting literally dozens. I will probably keep chiming in 
I preferred Ardal O’Hanlon myself. But Miller was good also. I do not like the new guy, too whiney.
You have to go back in time and dig some Young Ones. Also, Foyle’s War is pretty good.
If you’re going to check old British TV shows, I’d also go for The Prisoner, UFO, Yes Minister, Red Dwarf, and Oh, Brother! and its sequel Oh, Father!
Only if one likes schmaltz. We did make it through several seasons, but were finally overcome by nausea.
It’s not British, but the Australian series “Rake” is on Netflix. If you enjoy seeing a main character who has no redeeming characteristics, this is the one for you. He’s a divorced, coke-using alcoholic lawyer who would screw a knothole. But it’s fairly amusing for all that.