Four marine iguanas were received at the end of 1932; I don’t know exactly how long they lived but I doubt it was long.
The species is mentioned in the 1933 guide; according to the 1934 guide there is only a single specimen in the Reptile House; the 1935 guide doesn’t mention marine iguana at all. (If such an unusual species were still in the collection, it would probably feature in the guide so I assume that none were there when this guide was published.)
I don’t know off-hand about the flightless cormorant; I would need to do some further checking.
Thanks, Tim. It sounds like the iguanas didn't do very well in captivity in London, as with the rest of the world's zoos. No worries on the cormorant.