For the first time ever I entered the Central Line at Shepherd's Bush. Just
before I went down the last set of stairs to the platform, I saw a closed
exit and what looked like a tunnel going across a set of tracks.

This is the access to one of the two former lift landings. The other lift landing now serves as a passageway leading to the emergency staircase, which (unusually) are built in part of a former *lift* shaft. The original emergency staircase shaft, and some of the lift shafts, have been severed by the escalator shaft, which runs right through where they used to be.


As I got down to the eastbound platform, I could see thru the metal grating
what looked like another platform/tunnel but about 6/ feet higher than the
platform I was on. Could see power cables etc.
Any idea what this is?


This is a draught-relief heading, which connects to the disused passageway you mentioned initially, and, therefore, to one of the former lift shafts which hasn't been cut through by the escalator shaft.