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Unfortunately, the majesty of the Ruislip Woods National Nature Reserve,
is,
essentially bounded by residential areas.
The River Pinn, into which that stream, (Beech stream), with the two leaky dams,
ultimately flows, only has about 5 miles upstream,
of Eastcote, Pinner, Pinner Green and Hatch End.
Downstream from Ruislip we have,
Ickenham, Hillingdon (Circus), Uxbridge, (St. Andrews village), and Yiewsley
where it joins the River Colne.
So not a lot of space for beavers to expand into.
The Colne could conceivably support a beaver population,
as it arises in London Colney, (south of St. Albans),
and flows through much more farmland/local nature reserves/golf courses,
and,
road names reveal a previous era of wildlife,
like Otterspool Way northeast of Watford.
Have you tried introducing beavers? Nice work there, we could do with more leaky dams to slow the run-off.