Well, Mary has 5 months between Elizabeth's death and her own to try and endorse her chosen heir. Is Philip around, what would his view on the succession be?
Wasn't Margaret Lennox in favour during Mary's reign? Margaret is English-born, is in England when Mary dies, and has two sons- this possibly advantages her over Mary Queen of Scots. She's probably also better connected amongst the English nobility given her time at court.
On the other hand, if the Queen of Scots is unmarried then numerous nobleman will be dreaming of marrying her and claiming the English throne (is Norfolk between his first and second wives at this point?). If she's married to a Frenchman (who? There's no one in the immediate royal family who's the right age) I imagine that might take away some of her domestic support. People would also be weighing up the pros and cons of a union with Scotland.
The Protestants have teenage Catherine Grey.
If you want a male candidate you have to stretch a little...
- There's assorted Poles around, descendants of George of Clarence, would their uncle Archbishop Reginald apply influence on their behalf? But they're pretty lowly- they're not even titled.
- There's Henry Hastings, at this stage heir to the Earl of Huntingdon, who is a descendant of George of Clarence via the Poles, and was suggested as a successor by the Protestant faction when Elizabeth was ill with smallpox in the 1560s. Though he doesn't appear to have particularly wanted the throne.
Both of those would be pretty flimsy. One could also skip over Margaret of Lennox in favour of her 13-year old son Darnley.