I wonder if there ARE any experts on jet condensers theses days? I wouldn't bet either way, and while I know quite a lot about vacuum systems, jet condensers are certainly outside my competence.
If the water supply pipe to the jet is getting hot, it says that not much, if any, water is flowing through it. It isn't mentioned as to whether that water is pumped, or sucked in under the vacuum produced by the air pump. Assuming the latter, then a crack in the condenser casing would, as Mike says, drop the vacuum and do as is mentioned. There are other possibilities though: if the water inlet jet is partially blocked, it could be that the condenser gets enough canal water into it to apparently work when it's cool, but not enough to keep it that way. The other main possibility is the air pump: it's quite possible that it isn't pumping as well as it should.
Given that the condenser jet and pipework have perhaps had canal water flowing through them for years, I would dismantle them and check them out first, obviously giving them a good clean.
After that the air pump needs checking out next. It will do the main engine no harm to exhaust to atmosphere, given some temporary pipework so that the engine room doesn't get filled with steam. If this is arranged, it should then be possible to shut off both the steam inlet and the jet water inlet to the condenser, and see if a reasonable vacuum can be achieved. If it can't, then either the air pump is excessively "tired", or air leaks into the condenser are too big. Don't go with just my opinion, but I think that a condenser should never get all that hot, and it may be possible to seal cracks using an ordinary silicone sealant. I obviously don't know what seals and valves are employed within the air pump, but I will hazard a guess that dating from 1920 that rubber O-rings etc. are unlikely, and it may rely on close fitting metal pistons and valves, or just possibly oiled leather or other packing. Unless the air pump has had a major overhaul fairly recently, it's probably a good idea to give it one. Vacuum pumps CAN be extremely long lived, but pumping a mixture of air, condensate and canal water doesn't sound good for life to me, and I would guess that an overhaul ought to be considered annually, whether or not it has been used much.
Perhaps it would be better to disconnect the air pump inlet, and put a blanking fitting over it with a vacuum gauge before checking the condenser chamber for leaks. If it doesn't pull a good vacuum with only that connected, it really does need an overhaul.