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Yep, always ignore this one too. In my head, the signs are put there on account of the entitled rich people who live in the mews. They allow themselves to drive their Range Rover in, but feel it necessary to make cyclists walk...
Now the thing that grinds my gears are the cyclists that whizz along the riverside in Wandsworth park with no thought for the people walking with children / dogs. I've gone full apoplectic at one for nearly mowing down my daughter on her balance bike. He seemed to be complaining she didn't shoulder check before changing her line...she was two years old and yet he was convinced he was not in the wrong. People baffle me.
I've always wondered what the history of that place (Blade Mews) is.
My guess is that the land was sold off for development with the requirement that access to the park is maintained (rather than blocking off that gate). But the "no cycling" signs that have been put up aren't just advisory. (Behind Blade Mews there's an odd section of path that's part of the park but gated off.)
There are even no cycling signs that look like they apply to the public road next to the private bit: https://goo.gl/maps/58wrhSjJtvR2
It's one of the few signs that I ignore most of the time. (The other one is the no cycling sign on the little bridge over the tube tracks between Keswick Rd and Clockhouse Pl.)