As a very broad-brush answer, yes. They nearly always feature a deeper level of knowledge than your average American history documentary. (As do other British ones from Channel 4.) There is no such thing as total freedom from bias: that's a basic lesson of historical methodology! It may simply be bias by selection or favouring a British perspective on events. Those with presenters who have at least a Masters in history (and plenty feature professors and other history professionals) are the most accurate. In general most BBC documentaries are accurate, but laziness can get into the narrative of some where the presenters are there for flamboyance more than qualifications, for example those with Francesco da Mosto (which if the viewer is partial to silver fox men, may still have entertainment value). A few presenter-historians have well-known political leanings; for example, Niall Ferguson is conservative.

Older documentaries tend to be best for a serious amount of hard facts. "Civilisation" from the late 1960s is still considered a classic of the genre, although its upper-class bias will be more evident now. The good recent ones tend more towards the experiential, with more material on social history. Personally, for this sort of social history and sometimes irreverent approach whilst retaining scholarly accuracy, I would recommend Lucy Worsley, Mary Beard, David Olusoga's recent series Black and British, and the historical farms series and others from the same team (Tales from the Green Valley, Victorian/Edwardian/Wartime/Tudor Monastery Farm, Secrets of the Castle, Full Steam Ahead). There are so many others, though. I have certainly seen some bad ones, can't remember specific titles, but in the second half of the 90s and early 00s, there was evident 'dumbing down' compared with earlier series, but later as the new style such as those above found its feet, things improved again.