I’m not an Anglo-Saxonist specifically, but I have lectured on this relatively recently, so I can speak to this question broadly and also offer some advice for further reading. I would say in broad brushstroke terms, that the show’s accuracy is relatively sound. The Danes were invading the British isles in the ninth century, the battles represented (such as Edington) were real historical battles, and so on. Alfred the Great’s characterisation is reasonably reflective of what we know about him (particularly his scholarliness, holiness, and illness, which historians tend to think may have been Crohn’s disease or a similar gastrointestinal issue). Guthrum was a real historical person who did convert to Christianity. The violence and rapacity of the Vikings is reasonable, and their beliefs are portrayed fairly. The most famous representation of the Vikings is in the travelogue of Ibn Fadlān, which can be read about here: http://www.vikinganswerlady.com/ibn_fdln.shtml The author of this website gives part of Ibn Fadlān’s text in English translation. Ibn Fadlān was a Baghdadi traveller to the kingdom of the Kievan Rus’, who were Vikings. Admittedly, there may have been cultural variation between those Vikings and the others who went to the British isles, but nevertheless Ibn Fadlān’s descriptions of them are justifiably famous. One thing that bothers me about The Last Kingdom’s representation of Alfred is that it downplays his warrior-ness, and makes him appear a bit paranoid. Part of the reason for this is that they play up Uttred as the warrior hero for dramatic purposes. Uttred is a fictional character taken from the original books by Bernard Cornwall.

In terms of resources, try Daniel Anlezark’s 2017 biography of Alfred. For primary sources, Asser’s life of Alfred should be your first port of call. Others are mentioned by Anlezark and can be followed from there. His book is scholarly but also accessible in its writing. One detail the show gets wrong is that Asser himself was Welsh, and not Cornish. There are plenty of translations of Asser’s life of Alfred.