You probably are aware of Vera, Agatha Christie adaptations and series, Shetland, and Father Brown Mysteries, but there are so many other cozy mystery tv shows on Britbox in this category!
Britbox: the Best Cozy Mystery TV!
Sister Boniface Mysteries is a spin-off from Father Brown and therefore set in the same time period. It takes a bit to set itself up firmly as an independent series but by the end of season 1, you'll be adding it to your regular rotation.
Sister Boniface is a nun who assists the police and pretty much solves the crimes on her own. She is a woman of faith AND science, using her status as a nun and her PhD equally. The writers have done a good job of building side characters without having their stories overtake the main plot. It's all very cozy and intimate, set in a fictional village in the Cotswolds named, what else, Great Slaughter. Season 2 has just ended so sit back and marathon!
Another cozy favorite is Shakespeare and Hathaway: Private Investigators. Pay special attention to the titles for each episode. That's all I'm going to say about that! The friendly chemistry between the two leads builds organically, unfolding from a bit of a clumsy pilot but gaining credibility as the seasons progress. They hit their stride in Season 2. You'll like their employee Sebastian but the actor is so good that sometimes he outshines the leads!