wz662, the Nimrod and the Shackleton before it did not carry parachutes. As Maritime patrol aircraft it would have been assumed that any emergency would have been over the sea. Crews in a sea survival situation would probably survive better in a multi-seat life raft rather than any number of dinghies scattered far and wide.
Then the operational life was probably largely expected to be at 1000 feet or less with an emergency probably being related to a bird strike. The Nimrod was capable of flight on a single engine and could climb, at weights below 142 000 lbs, at 100 feet per minute. If it could fly and indeed climb then the need to abandon would have been low.
However the Nimrod was also assumed to have a lousy ditching capability. Sliding its tail along the surface it was expected that the nose would then hammer onto the surface at about 25g, kill the flight deck crew, break off, and flood the fuselage. Ergo there would be no need for immersion suits either, besides which they would be uncomfortable and restricting on a 9 hour flight.
After the ditching of the Dutch Atlantic and the saving of the crew, who all had once-only immersion suits, there was a successful reappraisal and once-only suits were provided. The orginal logic about parachutes persisted. I suspect the door positions in relation to the horizonal flying surfaces also suggested that bailout was not an option.
On the E3 of course it does not operate at low level, spends sometime over the sea and some over the land and also has a proper parachute exit (a la KC135). Given its role - combat support, the reliablity of its engines, and the proven airframe, it is obvious that parachutes are not needed in the E3 either. In the Elmsdorf crash parachutes would not have assisted crew survival. In the Nimrod bird strike crash in the 70s they would not have helped either.
In the MR1 at St Mawgan or the R1 at Kinloss parachutes would have given a very useful insurance and reassurance to the crews, provided they had a proper bailout exit.
The forgoing is not gospel, simply supposition on my part.