Is there scholarly concensus on the historicity of Foxe's Book of Martyrs?

No, there is not general agreement as to the exact historical accuracy of John Foxe's work. The majority of events are considered to be historical and widely accepted to be based on good sources such as eyewitness records, however doubt is often cast on the retelling aspect.

The primary accusation brought against Foxe's Book of Martyrs (originally titled Actes and Monuments) is its strong anti-Catholic bias. The doubt cast on the work is almost always the possible "spin" placed in the selection and retelling in order to elevate Protestantism as the true faith at the exclusion of other Christian sects.

• It is widely accepted that Foxe's selection process excluded martyrs of any sort whose primary allegiance was to the Catholic church. The standards for what he considered to be a true martyr were heavily influenced by his own doctrinal position. This doesn't mean that the cases he did select to tell about are actually not real cases, but it does keep his work from being considered a broad treatment of the issue of martyrdom in Christianity.

• His doctrinal bias comes through quite consistently in smaller details in the individual telling of stories. It is in this that the historicity is most to be questioned: that the events happened is typically not in doubt but the generous amount of fiction added to the narrative and possibly leaving out relevant details that didn't fit the picture he wanted to paint leave the exact accuracy of the work as suspect.

The Wikipedia article, which notes in the summary section the sometimes polemical tone of Foxe's work, has an entire section devoted to his merits as a historian. Here is one excerpt:

The author's credibility was challenged as soon as the book first appeared. Detractors accused Foxe of dealing falsely with the evidence, of misusing documents, and of telling partial truths. In every case that he could clarify, Foxe corrected errors in the second edition and third and fourth, final version (for him). In the early nineteenth century the charges were taken up again by a number of authors, most importantly Samuel Roffey Maitland.[42] Subsequently Foxe was considered a poor historian, in mainstream reference works. The 1911 Encyclopædia Britannica accused Foxe of "wilful falsification of evidence"; two years later in the Catholic Encyclopedia, Francis Fortescue Urquhart wrote of the value of the documentary content and eyewitness reports, but claimed that Foxe "sometimes dishonestly mutilates his documents and is quite untrustworthy in his treatment of evidence".

The article goes on to cite individual cases of criticism and includes sources identifying the major critics and their works.

According to the Catholic Encyclopedia, several contemporary church figures were among the first critics of his work. They also give several sources for additional studies critical of Foxe:

The most careful examination of his methods is to be found in Maitland, Essays on the Reformation in England (1849), and in Gairdner, History of the English Church from the ascension of Henry VIII to the Death of Mary (1903); Lee in Dict. of Nat. Biog. Gerard, John Foxe and His Book of Martyrs (Catholic Truth Society, London), includes the opinions of a number of Foxe's critics.

To be fair, Foxe's critics themselves are not without their own critics. Since the majority of those who oppose his work do so in defense of the Catholic church (often pointing out exacerbating circumstances in some of the deaths that weren't always purely religious in nature or the fault of the Catholic church) we can in fact conclude that there was also some accuracy to his work. While it might only have shown one side of the story, knowing that the primary point made by the other side was that he left out a whole set of martyrs and cast too much blame in one direction, we can actually conclude that much of what he did write is indeed grounded in history even if his telling of it is polemical.

It seems likely to me based on the extended controversy that some or many of the stories told would not pass muster by any credible historian or journalist standards due to the large number of aspects that are dramatized. This does not, however, mean that the actual events were not historical and possibly just as —if not more— dramatic than the re-tellings.

Whatever the exact circumstances, that the basic events happened is not really in question.