PADI qualifications (even to Rescue Diver) are really basic qualifications too a low standard and are not likely to be of much use in your military training other than to show that you are genuinely keen on diving. You don't do any deco, no overhead, no navigation to speak of, no low vis or night, no standards to meet in even simple tasks like buoyancy control or different finning techniques, no underwater signals, rope work etc.
If you wanted to learn skills that might help you pass the RN diving courses you would have to spend a lot of money getting serious TDI or IANTD technical diving qualifications. If you trained up to say TDI Trimix on open-circuit doubles, got qualified on 2-3 different rebreathers (say Draeger as used by FDU, Meg as used by USN, Poseidon as used by some other Nato navies like Germany and Sweden) and did some serious overhead diving like TDI Full Cave or TDI Advanced wreck, then you might have skills that would be helpful - as long as you could keep your mouth shut and relearn everything the RN way. But you would be looking at an outlay of about £15-20k over a couple of years to work your way through that lot. I say might, because I am not an RN diver so don't know what their standards and training is like, other than occasional chats with FDU divers at technical shows, but I expect it is too a high standard.
If you don't have the time/money for technical diving then I would agree with Muggle. Eveything is easier if you are massively fit - that doesn't cost anything. Do as much diving as you can, and try and get some training from an experienced technical diver on trim, buoyancy control, efficient finning as most recreational divers are just appalling at even basic skills like that.
On the subject of chamber tests, I was diving with a former Russian navy diver recently and he told me a bit about their training. Apparently, of several hundred volunteers, only a small handful make it although training. They are expected to tolerate ppO2 of 3.0 (USN go to 2.0, civvy divers usually only go to 1.6). So to whittle down the numbers, they stick everyone in a chamber and pump it up with oxygen and see who spasms first.