What it looked like in the 1650s thanks to Classical fronts added by Inigo Jones from 1633
A digital reconstruction of what it would look like
(both pics from wikipedia)
Most likely, one of two options: it either gets left as it is - a la Notre Dame de Paris - or it gets overhauled piecemeal - like St. Peter's Basilica (unlikely since St. Paul's isn't a cathedral, only a basilica; Rome's actual cathedral - San Giovanni in Laterano - was restored in the 18th century, given a new façade and otherwise left as is). And, then, when the Victorians come along, most likely they do what the Romans did to the bell-towers added to the Pantheon, and remove anything which isn't "Gothick" and probably make a few additions of their own.