The only possibility in Foster is: Shuckburgh, Edward, s. Charles, of St Martin's-le-Grand, London, baronet. Christ Church, matric. 28 Nov 1722, aged 18; BA 1726, rector of Bromsall, Staffs, died Feb 1730.
But this does not fit with the fact that he is described as of All Souls and a fellow there in 1728.