I've commented on Tuchman as a historian before (the gist is that her methodology is flawed, presentist and sensationalist) and while I cannot speak for Ian Mortimer he is at least working with the benefit of a modern historiography and in this instance is echoing (if slightly overstating) the modern consensus. The two chief sources (Jean de Bel and Jean Froissart) agree to a point then diverge.

Connie Saunders argued persuasively that the source of this rape (Jean de Bel's Chronique) echoes quite consciously the literary rape of Lucretia. Both Froissart and Jean de Bel state that Edward, upon meeting the Countess, was overwrought with love and urged her to receive his love (to put it euphemistically). The Countess replied:

si je le faisoie, vous m’en devriez blasmer, non pas blasmer, mais faire mon corps desmembrer

You should reproach me if I did this, no, not reproach, but have my body dismembered

Chronique de Jean le Bel, ed. Jules Viard and Eugène Déprez, 2 vols, La Société de l’Histoire de France (Paris: Librairie Renouard, 1904 and 1905), i, l.293.

Translation (and this response in general) from, Connie Saunders, Rape and Ravishment in the Literature of Medieval England, (Cambridge, 2001), p.174.

While Froissart has the king override his desire to 'constrain' the Countess and subsequently drops the story after mentioning Edward's invitation that she attend a tournament at London in 1342, Jean de Bel recounts how Edward, after another rejection, enters the Countess's rooms and rapes her while she was in London.

When the Countess reported this to her husband (again following the narrative of Lucretia) who confronted his king and was forced by Edward to relinquish his lands and departed on crusade to Iberia where he would later die.

The historiographical defence of Edward was made by Antonia Gransden in 1972 (Tuchman's work was published in 1979 - this was another pertinent criticism, she had an outdated bibliography and historiography even then, let alone now!). I don't have access to the article right now so I'll quote Saunder's explication:

Antonia Gransden suggests that this memorable but uncorroborated episode [in Jean le Bel's Chronique] functioned as a piece of French propaganda against the English soon after the breach of the truce of Malestroit. She explores the correspondence between the narrative and historical records, to find various inaccuracies in le Bel’s account, such as the name of the Countess, the dates, and the details of the death of the Count, which occurred not in Algeciras but in Windsor, and not in holy wars but in a private feud. Gransden notes too le Bel’s emotive and colourful prose, and the lack of evidence for the speeches. The alleged rape served as a means of blackening Edward’s character and also, perhaps even more damningly, of equating his rule with that of the Tarquins. Like the Lucretia story, the episode illustrates abuse of power on both a personal and public level.

Saunders, Rape and Ravishment, pp.174-5.

I hope that's helpful, and should you wish to read Gransden's argument for yourself the article is:

Gransden, A., ‘The Alleged Rape by Edward III of the Countess of Salisbury’, English Historical Review, v.87 (1972), pp.333–344.

[edit: replaced thread link with permalink to my comment on Tuchman]