Agnes Nutter, witch, is considered the only person to have ever written an accurate book of prophecies in the history of humanity (before she blew up her entire village for burning her as a witch, her predictions may have been "nice" but her revenge wasn't). And she has predicted that in a certain year, on a Saturday, the 11 year old anti-Christ will destroy the world. Angel Aziraphale and demon Crowley have grown to rather like the Earth in it's 6000 years and want to stop this but, there seems to have been a mix-up over who the anti-christ really is....
Perhaps it was a mistake to read the book first since I ended up preferring the book to the radio drama to such a large extent that I'm not sure I really enjoyed the drama. I felt like the story lost its most amusing bits since they were in the exposition and details, the things that are read but not spoken aloud by the characters. The drama made an effort to include some of those details in but usually they just came off as awkward, such as when Crowley suddenly talks about his design plans with the highway encircling London to two cronies who very obviously don't care (plus, the details that made this plan so amusing had to be omitted so the entire joke fell flat). In the original book, the not-quite-a-narrator felt very Diana Wynne Jones-esque, the book was filled with descriptions with some commentary but you never felt as if it was an actual person telling you these things, it was just as if you were there with a very snarky and observant mindset.
As in the original, the story focuses on Adam much less than it seems like it should have. In the end, Crowley and Aziraphale have no effect on the outcome of the world at all and yet it seems like Gaiman and Prachett liked these two characters much much more than Adam. He's still fleshed out well enough here to understand why he makes his choice (again, a lot of the details about what he was thinking were written not spoken so you miss just how much Anathema s literature on saving the whales and such really affected him) but it still seems as if he should have been the main character here and was shunted off. While I was reading the original book it reminded me a little bit of 20th Century Boys actually; between it's shifting viewpoints between kids and adults in a situation that seems like it was thought up by a pre-teen boy and it's slightly dated setting (the radio drama does gracefully bring it up to the current year) there was just something similar to the story, although the tones are wildly different. Here with the reduced viewpoints and more straightforward story I had completely forgotten about that comparison until I started writing this.
So, the radio drama isn't terrible, the story is fine, the acting is nice, and it's adapted well enough. However, I preferred the book and would recommend that one first. BBC did have the radio drama streaming free worldwide on their website but, since I actually got to the show a bit late, the first few episodes have now been removed from it. If you've started and haven't finished yet, yes go do so, if not I would imagine the BBC will make it available for sale online later on and hopefully put up a teaser so you can try before you buy at least a little bit of the show.