I tried the public pump on Monday evening. There's nothing decent to lean a bike against (the pump is a smooth metal cylinder). Fortunately, I have a propstand on that bike. The valve head was good (a solid Topeak attached to braided hose protector). But the amount you can move the pump handle is severely limited, as it is so high. I managed to get up to 80psi. It didn't seem to go any higher. I checked the head was securely on the valve (it was). But the pump wouldn't get above 80psi, and it just didn't get harder, so I suspect it wasn't compressing much, if at all.
I rode home through Richmond Park with an underinflated tyre