Looks to me like there's still at least a partial cavity. I wonder when and why it was filled in? I imagine it became dangerous at some point after the railings were taken down during the war, and there wasn't such a need for it anyway, as people could get from one side to the other at ground level quite easily.
EDIT: Aha! Found this snippet when I was researching something completely different, of course. From the ever-helpful CHIS website:
When there were railings all round the garden and down the central path, in order that the children could play together in either garden there was a tunnel for them to go through. This was filled in during the 1970s but almost at the south east end of the path if one looks over the low wall the top of the arches can still be seen.
GPS Coordinates:
51.45544, -2.61576
Location: Clifton Village