The Standard Conduit consists of 220 feet of passageway which fed a conduit house located 84 feet behind the Standard Reservoir building. That passageway is entirely separate from the Hyde Vale Conduit, and is several metres higher. The small conduit house of the Standard Conduit is shown on the 1894 OS map, although it disappears by 1914:

Countless writers and researchers over the years have confused or conflated the Standard Reservoir, the Standard Conduit and the Hyde Vale Conduit.
The Hyde Vale Conduit originally drained into the Standard Reservoir, which I found surprising because the Reservoir seems to be at a higher level than the floor of the Hyde Vale Conduit along which the original lead pipe/s ran. However, the 1780 survey is fairly clear on this point:
Returning to the Standard Reservoir, one other Branch of Supply is a large leaden pipe, which lyes underground, was traced to a door in the face of the hill, at the end of a large brick arch, well constructed - Which arch passes from thence, out of the Park, under Croom hill, under the public highways to a hollow or valley, commonly called Sots Hole, or Conduit Vale...
There is no entrance to passageway inside the Standard Reservoir building, which simply covers (albeit grandly) a large lead-lined cistern fed by at least 2 pipes uphill of it. The Hyde Vale conduit has its own entrance in the hollow nearby.
Immediately uphill from the Standard Reservoir building is a second (much bigger) underground reservoir fed by a pipe from the Standard Conduit (see map below); this was opened at the beginning of World War 2 for consideration as an air raid shelter. Again, there is no access to passageway from this structure.

The 1780 Admiralty Survey describes the Standard Conduit concisely:
...a Conduit Head on the face of the hill just above the reservoir 84 feet distant, which, for the sake of distinction, was called No.1 - This Conduit-head has a small receiver in it, and collects water from one brick drain underground, about 120 feet in length, which extends eastward, to the roots of a thorn tree, and also from one other brick drain underground, about 100 feet in length, extending south westward, in a curved direction, to a hollow in the ground.
The passageway of the Standard Conduit is almost certainly still there; it just needs re-opening. Half an hour's spade work would accomplish that, but unfortunately the Royal Parks have repeatedly refused any systematic investigation into the conduits, despite their considerable historic importance.