I disagree, Mary didn't succeed because people were sick of war, Mary succeeded because there were no male alternatives.
When Henry VIII created his Third Succession Act (I believe in 1544), 7 of the first 8 people in the line of succession (which favoured the descendants of his younger sister, Mary, over his elder sister, Margaret) were female. The only male descendants of Henry VII's alive at the time of Henry VIII's death were Edward VI and Henry Stuart, Lord Darnley, who was 2. Henry Stuart would have been 8 when Edward died, meaning that the choice for the succession was either a woman - Mary, as named by Henry, or Jane, as named by Edward - or else an 8 year old Scottish boy.
Things were very different in Elizabeth of York's time. There was never any real consideration of Elizabeth as a potential monarch, as any claim she would have had was immediately superseded by her uncle Richard. She was also declared to be of an illegitimate line - Richard used as his justification the idea that Edward IV's marriage to Elizabeth Woodville was invalid and therefore their children were illegitimate (not to mention the rumour that Edward himself was illegitimate).
During Elizabeth's time there was no point when she could have been declared monarch, nor would she have likely gathered any support had she done so. She was what, 18 when her father died? And female? And instantly facing a war with her uncle over the succession? Not to mention the Lancasters? In the mind of the 15th century individual, a woman could barely lead the country, let alone do so in a time of Civil War.
Adding to that was the fact that there were far too many possible male claimants. There were her brothers, whose deaths weren't clarified. There was Richard III, who had himself declared king. There was Edward Plantagenet, the only son of the brother in between Edward IV and Richard III. There was Henry Tudor, the Lancastrian claimant. There were too many male options to chose between to consider supporting Elizabeth as a viable option.
That Henry VIII went out and deliberately named his daughters (and nieces) in the line of succession while Edward didn't becomes a matter of "what if." While that would have given Elizabeth a claim, it also would have endangered her life. Richard III had no problem with at minimum locking up Edward IV's sons, and likely having them killed, and may very well have done the same to his nieces had they been named in a succession.
I don't believe any woman was named in the line of succession between when Henry I named his daughter his heir and when Henry VIII named his daughters as in the succession. Between the two, however, there wasn't ever any lack of male heirs. What the situation that evolved after Matilda's failure to succeed to the throne was the fact that women couldn't inherit, but men could inherit if they were descended from the monarch in a male line - Stephen could inherit through his mother, who was still alive when Stephen became king, as could Henry II or Henry VII (whose mothers were also still alive), but not their actual mothers.