There were few seekers in the 1540s – and I’ve found none at all in the short reign of Edward VI. In theory sanctuary was still operating in the sanctuary cities and parliament tweaked the legislation twice, suggesting it was being used. But no actual records of cases.
Perhaps unsurprisingly, though, there was a small resurgence during the reign of Mary, though evidence I’ve seen indicates that the revival was confined to a single sanctuary, Westminster Abbey, likely as part of the revival of monasticism there — with the exception of this case. Though other 1550s cases all relate to Westminster Abbey, there was one somewhat confused murderer in 1555 who didn’t get the (many) memos about sanctuary over the previous several decades.
In January 1556, amongst the issues discussed at a meeting of the Privy Council was the escape of one Thomas Burley, who’d been convicted of intentional murder but had then escaped from Newgate prison before his execution.
Instead of running to Westminster Abbey, as might have been sensible, he went to the liberty of the Savoy, a bit closer to Newgate. The Savoy was an asylum for debt but hadn’t served as a sanctuary for felony either before or after 1540.
Not only had he gone to a non-sanctuary, but his offence probably also made him ineligible for the privilege: he’d evidently already been tried and found guilty of “wilfull murder,” one of the excepted crimes by the 1540 sanctuary statute (under Mary was this observed? not observed? who knows.)
So Burley’s bid for sanctuary was really just a bad idea. The Privy Councillors wrote a letter to the Master of the Savoy Liberty, telling him that he needed to find Burley, arrest him, and hand him back over to the keeper of Newgate prison.
Acts Privy Council, 5:220-21