In message id, Dr J R
Stockton writes

I've misplaced a better answer; but the unused hole is a bit over one
train-width to the north, and a few yards to the east, of the working
one. The ends are easily seen.

Ah, got it!

When built, both tracks of the Kingston loop buried under the main line
at Elm Road, and then ran in parallel with (but independently of) the
main line (i.e. on what are the southern pair of the four tracks). So
the mysterious hole was for the Kingston Loop up-line before the main
line was re-arranged for four-track running through to Surbiton. I'm not
sure when that was, but it would have been when the Kingston up-line was
re-routed across the rather awkward level crossing at Elm Road and on to
the north side of the main line, thus leaving the unoccupied short
tunnel under the main line.

According to the Middleton book on the Kingston loop, the old up-line
track was there until about 1884. It can be seen (using the magnified
view) at:

http://www.old-maps.co.uk/oldmaps/in...orthing=168482

--
Paul Terry