I just watched the pilot episode of the last kingdom, and I thought it seemed quite accurate (though i'm not a historian). What do historians who have studied that period think about it?
The books that The Last Kingdom is based on is historical fiction where the author places fictional characters into historical settings. The authors note at the end of the books details how he has diverged from the actual historical events he has researched. Uthred of Bebamburg is fictional but in a later time period there would be an Uthred.
You may be interested in a recent podcast in which the author of the source historical novels, Bernard Cornwall, talks about the series, including on its 'accuracy' and his sources. The podcast is called History Extra and the episode The Last Kingdom and Agincourt. I think it's a BBC series
Late answer, my professors have said that it really isn't very historically accurate.