I've been out this evening, but I've traced the porch-holding-up-the-West-Front argument back as far as 1859:

The porch ...materially injures the uniform effect of the front; but its insertion seems to have been rather a question of necessity than of taste. It was probably erected "as an abutment against the west front, which, by a bulging outward of the pillars or a settlement of the foundations, was falling forward toward the west. It was, in fact, overweighted by the stone spires and pinnacles of the flanking towers, which those structures, having no proper buttresses, were ill adapted to bear. The construction of this elegant little edifice is extremely scientific, especially in the manner in which the thrust is distributed through the medium of the side turrets, so as to fall upon the buttresses in front. These turrets, being erected against one side of the triangular columns, on the right and the left hand, support them in two directions at once, viz. from collapsing towards each other, and from falling forward. The latter pressure is thrown wholly upon the buttresses in front, which project seven feet beyond the base of the great pillars."

Handbook to the Cathedrals of England, 1862, quoting F. A. Paley, "Remarks on the Architecture of Peterborough Cathedral", 2nd Ed, 1859.

On the other hand, the definitive modern book seems to be An Architectural History of Peterborough Cathedral  by Lisa Reilly .  At a mere £165 on Amazon, I don't suppose I'll be buying it any time soon. However, it could be significant that, although every review and excerpt I've found mentions the porch, none has referred to its supposed structural function.

I wonder if the library has a copy....