I can see why the first novel, which
kathyh gave to me, has blurbs with Le Carré comparisons, and there are literal Le Carré shoutouts in both the novel and in the tv show, what with Grandpa Cartwright cheering up River by pointing out how many times Smiley came back: Slow Horses is definitely in the school of "secret services are full of pathetic screw ups, they do dastardly ruthless stuff just like the ones they're fighting, and also fixing their own mistakes causes as much, if not more trouble than the nominal opposition does" along with the double and triple twists of the narrative revealing that while you thought what's going on was x, all the time what's really going on way y, and maybe y and z, and the clues were there!" Which if done well makes for compelling stories, and this tv show (I've only read the first novel and just finished marathoning all three seasons) is done very well. Where it differs from Le Carré is the far more overt black humor, plus no character is into German literature, there are more important female characters and way less digs at the Americans; in fact, the overseas cousins might as well not exist in terms of plot and screen/page relevance. (This is also one of the big differences to, say, Spooks, where you can tell the Howart Brenton origin from the Americans are the worst!" dogma.)
The basic premise: "Slough House" is where MI5 agents who are deemed have fucked up too often (and who don't have enough useful connections) are banished to, in the hope that the sheer awfulness of their existence there will encourage them to quit/retire; as civil servants, they're very difficult to get rid of otherwise. It's headed by Jackson Lamb (Gary Oldman as the anti-Smiley in manners but not in hidden-at-first-glance competence; the performance is also the exact opposite of Oldman's Tinker Tailor Spy the movie one), who used to be a big thing at MI5 until for reasons later revealed he ended up in Slough House, and each season sees our (anti)heroes engaged in some humiliating task which then turns out to be important and/or involves them in the kind of suspense filled adrenaline pumping operation the spy genre can't do without. My favourite among his staff is Catherine Standish, on-the-wagon alcoholic and chronically underestimated organizer and secretary. By season 3, Louisa has become my second favourite, though. As mentioned before, fighting terrorists or Russians takes only up half of the time (if not a third); the rest of the time is devoted to struggles with "the Park", MI5 Central, which is headed by a) Ingrid Tearny (Nina Sosonya, only present briefly in season 1, not at all on screen in s2 but in every episode of s3) and b, as "Second Desk" and present in all three seasons, Diana Taverner, played by Kristin Scott Thomas. Both Tearny and Tavener as presented as political animals looking for scapegoats to throw under the bus in their place when things inevitably go wrong, very ruthless and looking out for No.1., but Diana Tavener is the less worse in that she stlll seems to have some red lines and awareness that the Unwanted Crowd at Slough House are fellow agents, too (so far). They're also rivals with each other. This means you as the viewer can enjoy Kristin Scott Thomas verbally spar with both Gary Oldman and Nina Sosonya, the former on a regular basis, and it is great fun. The relationship between Lamb and Tavener comes across as my kind of "disdain for each other as people pared with grudging respect for each other's abilities and awareness they need each other" type, and I am very amused that they do the thing Terry Prattchet and Neil Gaiman parodiied in Good Omens the novel and which is definitely a fine long traditon of British spi fiction, i.e. having regular kind of secret meetings on park benches.
What saves the show from being as cynical as a lot of its main characters is that it very much respects actual human suffering. For example, S1 has an important kidnapping-and-threatened-murder plot, and while the narrative is satiric about the kidnappers, it never is about their victim. And what makes the titular "Slow Horses" (i.e. the agents who ended up at Slough House) easier to root for than their opponents is that they are still capable of compassion, and don't go for the "bad guys shouldn't be taken alive, only dead, because they're bad guys" school of thought (which, btw, is very much the norm in their genre. All in all: the show is very watchable to me, honestly more than the first novel was readable. (It's the narrative voice in the later that just gets me the wrong way, I think.)