Could someone do a mock-up of a Union Jack that just has St. George and St. Patrick? It'd be a hideous, hideous flag.
(only one I found on Google)
Does it have to be some variant of the Cross? Surely England and Wales can come up with a better flag than that, perhaps one inspired from the Welsh flag, only that it would also include a White Dragon (standing for Anglo-Saxon England) or the Royal Lion in addition to the Celtic Red Dragon on a blue background.
...Your proposal initially left me thinking you wanted St. George slaying the Welsh Dragon as the flag.