SEN can only be a CAT I airport because primarily the runway width (min for cat II+ ops is 45m, SEN is 37m) and largely the church is in the ILS critical area.
In addition, the current approach lights mean a slightly higher minima even for CAT I, the minima at the moment is 750m but minimum for a CAT I it usually 550m.
That said, over the winter there's very little call for anything better than CAT I so i don't think it's such a major issue.