When St Pancras station was being built the Metropolitan line passed in front and there was a potential plan to continue the widened lines, so a second tunnel was built. In 1930s this was extended west and a junction added (near Ossulston Street / Euston Road), the Met was diverted through it and a similar tunnel built for westbound trains on south side, the original running tunnel is now a concourse (and for many years had short sidings at western end). The Met platforms in the old station were closed when these opened.
The tunnel forks off the tunnel up to Kentish Town and runs under St Pancras forecourt, parallel to the Euston Road and the original Met tunnel, then stops at the boundary of the Midland's land on the east side of the road that runs up the west side of St Pancras station. It was built at the same time as the connecting tunnel as part of the initial work before the main station could be started, to make sure they would never have to dig any of that lot up again.
The Met eastbound was connected to the Up Widened Line just west of the Met station, I think in 1927? Then in the mid-30s (1936?) they knocked a hole through the side of the unused tunnel to the Met and inserted a section of single line from further back along the Met eastbound track to the junction with the Up Widened Line, so that eastbound freight trains on the Met for the Widened Lines could wait in the loop for a path over the WL without blocking the Met. This of course left a stub of tunnel still disused, from where they knocked through up to the actual end of it.
Then a few years later they moved the Met station to its present position. A platform was built alongside the loop line, which was realigned slightly to suit, and this became the Met eastbound line; the original Met was truncated at the eastern end of the station, leaving space for the passenger access; and the westbound line was diverted into a new, smaller, tunnel around the south side. Over the years the original Met tunnel was cut back further, in I think at least 2 stages, and filled up to platform level, for use as passenger concourse, leaving the short stub-end of siding at the western end that is still there. The unused bit of the spare tunnel is of course the bit of tunnel visible off the west end of the eastbound platform.
I have never been able to find any evidence that the spare tunnel was ever extended beyond the Midland's boundary. The name "Ossulston Street Junction" crops up sometimes, but it seems to be yet another of these infuriating instances of spacewarp cartography so common in the naming of railway features. Nothing starts to happen to the track until much closer to St Pancras. To extend the tunnel westwards would have meant digging right across the front of Somers Town goods depot, and the chaos would have left traces. Also, it would have meant excavating right up to the side of the hotel, and I can imagine them being distinctly unwilling to risk disturbing the foundations and bringing that lot down on top of their heads.
What they did was go through the south side of the tunnel leaving a blank end, thus dodging the hotel, and widen the Met tunnel to split off the connection. Then they just repurposed things a bit to turn it into a station. The eastbound track layout today is still remarkably well preserved, following the alignment of the original diverging loop line and then wiggling a bit further sideways just before entering the platform, where they had to realign the loop to get the platform in.
I assume there is no trace of this, or the access left?
It was in the point of the angle where the Hotel Curve tunnel diverges. As far as I know they've not had cause to rebuild that particular bit of tunnel wall since.