So, I had this thought on this matter:
Edward VI increasingly becomes convinced that he's not going to survive for long or long enough to have issue, therefore, he writes out his last will and also his declaration of who is successor is, using his father's example as precedent for this. In it, he confirms his nephew Edward Dudley as his heir under a regency led by the Dudley family, failing that, his successor is to be Charles Clifford, under a regency also. I'm thinking that when Edward eventually clocks it in 1553, Northumberland goes out of his way to ensure that his grandson is confirmed as the new King, having the lords of the regency council swear fealty to him including Clifford as well, and then sending men to arrest Lady Mary.