Blowup - Pic ref: bu038
I also walked the length (and breadth!) of Cheyne Walk looking for this property. Luckily, I found it to be no. 100 Cheyne Walk, SW10 0DQ (aka Lyndsey House), at the west end.
There's a bollard in the pavement outside the gate. As for the gate itself it has been 'filled in' (painted black, too) so that you cannot see through the gaps. I did try to contact the occupiers to gain access/entry, but they have not replied after two attempts.
Hope you have better luck.
Regards, Ian Bolton
P.S. Cheyne Walk is at bottom of pic