The Last Kingdom is an 8-part (mini) series produced by BBC and Netflix. The first season adapts the first two novels in Bernard Cornwell's The Saxon Stories saga. I am not familiar with the source material, so I will not make any comments about how faithful the adaptation is.
As a newcomer to the story I thoroughly enjoyed the show. What I appreciated the most was the fast pacing of the story; it was almost at break-neck speed. In one scene the characters were in north of England, and in the next scene, viola, they arrived at their destination in the south. Compare this with Game of Thrones; it takes characters almost a season to get from point A to point B. Of course Game of Thrones is one of the best shows in TV history, and even with the slow progression of the story, dialogue and acting are at the highest level.
Coming back to the Last Kingdom: the acting is great and action scenes (two in particular) are perfectly choreographed. Reference to real historical events is the icing on the cake... The protagonist, Uhtred, is a little annoying in the first two episodes, but you'll warm up to him.
As for negatives: the production design and costumes are not on par with the other components of the show. E.g. King Alfred has the cheapest looking crown that I have seen on the screen in recent years.
Overall, it's fun, fast, engaging, provides a great escapism to medieval times. 8.5/10