There are very very few books converted into TV series or films where you can say the TV series/ film was as good or better than the book.
IMO the Yes Minister and Yes Prime Minister TV series is one such rare example.
I got to see the TV series before I read the book. This was on the Indian national channel DoorDarshan which had a quota to show at least one English TV series during primetime. I was a kid and didn’t find it easy to find out exactly what was going on, but could follow this easily. After a couple of years of the first series they also had aired the Yes Prime Minister series
The book was harder to find – imported books were expensive those days, and except pulp fiction which were available in local versions, reference and special books like the Yes Minister were hard to find.
I got to read this several years later and it was such a delight, and I got to appreciate what actually was happening, all the machinations and tussle between the bureaucrats and politicians. And the book had a lot of other cheeky references (it was written in the future chronicling the political career of Jim Hacker the Minister and prime minister).
And around the same time the series was being re-run in one of the channels, and it was so much fun to watch again and this time around I was able to figure out what was going on. The TV series like the book achieved so much impact through simplicity and pithiness, and it was not loud like the American comedies, instead relying on witty dialogues and some amazing acting. In any episode there were barely more than five actors taking part, and then the locations would be barely two or three but it used to keep us engaged. What ran the show in addition to the superior writing was the fabulous acting talents of the entire cast. Not one would be out of place or character and fitted it to a T. You liked all of them, including the slimy bureaucrat who was played by the oily actor.
It also was one of the few TV series that managed to run a couple of seasons and maintained its standards. It also was a great revelation into the brit humour and lifestyles, and the spare times of the 70s where everybody pinched their pennies and maintained a very modest lifestyle.
A true test of a work of art is how much relevant it continues to be nearly three decades after it was first aired, and also grown in terms of appreciation. The Yes Minister and Yes Prime Minister series are just that.
My recommendation is that you read the books and then watch the TV series following that, and savour a timeless classic that set the standards for British TV humour and has not been surpassed as yet.