135 A is about the limit of what you can run off a 13A supply (although, as dbdb has implied, you can get away with a significant overload of such a circuit for short periods).
Assuming that switched spur box is fed from a spur off a ring main or a dedicated circuit on the CU and not another bodge, it should be capable of powering the welder. I'm guessing this was the original garage socket and the rest have been "tacked on"?
The only thing that would concern me, as AndyH has eluded is that, since the extra sockets have been added in a haphazard and illegal way, I'd also wonder about the standard of wiring employed, and we can't see that from the photo. I think I'd be happier plugging the welder into the socket next to the spur box, eliminating all the added wiring. Either way, the world won't end if it doesn't work, so try it.
I would, however, take Andyroid up on his kind offer, since I doubt that garage supply has an earth leakage breaker, and they are advisable, really, if using hand held power tools in such an environment, as are proper MCBs rather than wired fuses.