My intuition would be that, since the Connection as currently defined is placed in the "Ecology" section, it only applies to "natural" underground rivers.
It could of course be redefined - or else a new Connection created for "Man-made Underground rivers"!! My inclination would be to try for the latter.
Does the Tyburn actually flow "under" Westminster Abbey?? This Wiki suggests nothttp://en.wikipedia.org/wiki/Tyburn_(stream)
- rather that the Abbey was built on Thorney Island which was in the middle of a number of branches of the Tyburn. One of the links from that Wiki page states "The river's course was also drastically changed by the city. Instead of running toward the site of Westminster Abbey, it was channeled further south and ran into the Thames near the site of the Vauxhall Bridge"
. So, any Connection would need to be "once removed". e.g "Originally built on an island in the River Tyburn - which has since been diverted and runs underground".
And - are there another 2?
a. Paris Banks of Seine.
The original effluence of the River Bievre into the Seine was where the Rue de Bievre is situated today - situated on the south bank at the eastern end of Ile de la Cite. It has since been moved further east. See http://parisisinvisible.blogspot.com/2009/07/bievre.html
b. Kremlin and Red Square
the Western walls of the Kremlin were defined by the River Neglinnaya"The Kremlin was built on a hill west of the Neglinnaya, using the river as a moat"
(Wiki) and "At one time the River Neglinnaya, a tributary of the Moskva, flowed along here protecting the Kremlin walls. There were two bridges over the Neglinnaya, a drawbridge by the Pine-Grove Tower and a stone arched bridge linking the Trinity and Kutafia towers"
. The river now flows underground elsewhere and its original bed constitutes the Alexandrovsky Gardens which run alongside the Kremlin walls and are (probably??) outside the Kremlin WHS boundary - but still , I feel, "connectable" on the basis of the river's role in the placement of the Walls etc?
On re-reading this it might be better defined as
"Re-routed rivers - WHS connected with Rivers having undergone major man-made changes to their original location " (wording to avoid including sites with only minor adjustments!!)
If this is the case then I think that Vienna would also need to be included as I think that earlier beds of the the Wien River and Donaukanal are within the inscribed area (Assif??)