I seem to recall (a vague memory from a short newspaper report I saw some years ago) a 'moving barge' helipad being sugested a few years back - mid/late 80's(?) The various authorities along the Thames refused it permission to moor in their patch, so it wasn't a goer (if you don't have access to the banks, a helipad's not a lot of use). I assume the planners were thinking of the noise/'safety' lobby. I don't think it got to the point of any public enquiry.
Cars, buses, lorries clogging the streets and clagging the air? No worries, the more the merrier. Helicopters trundling up the Thames? No way! Perfect sense to me (not). But then I am biased.