You can dive into the docks at Canary Wharf from now until the end of October.
Middle Dock — directly below the glassy monoliths of Canary Wharf — might not be the first place you think of for a refreshing dip, but the body of water enjoys quite the following of intrepid swimmers. And where else can you go for a dip with DLR trains shuttling back and forth right above you?
What's more, the waters are described as 'crystal clear' (they're fed by spring water from deep below), which is more than can be said for most of the Thames.
You needn't be a hardened natator to take the plunge; swimmers of all experiences can dive in, although you'll need to purchase a NOWCA membership for £15 per year — and each swim session costs £9 per swim (regular free events are, however, offered to NOWCA members.)
If you're worried about hypothermia/shrinkage, the water temperature as of early July was over 16°C, so it's advisable to get a wetsuit/drysuit.
Swimming days and times at Middle Dock seem to vary (though it tends to be four-five days a week). Check out availability here.
By the way, your NOWCA membership also means you can swim in the nearby London Royal Docks.
More information on swimming at Middle Dock can be found on the Canary Wharf website, and on Love Open Water's.