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The sewer system can't retain enough when it rains heavily.
Similarly, the Thames is the overflow for the combined sewer system - when it rains raw sewage is discharged into the river. They are currently building the "super sewers" to increase capacity. Opponents say it can and should be dealt with instead by removing much more rainwater from the system, reducing impermeable surfaces, increasing ground drainage, green roofs and rainwater harvesting.
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Is the water quality of the Thames so good you can swim in it everywhere?
As others have said it depends on the weather. I've swum in the Thames without getting anything nasty. I tend to keep an eye on things like http://csoalerts.blogspot.com/ and would ideally leave it a week since a notification. I broke that rule last year for the Totally Thames swim (https://www.londonlive.co.uk/news/totally-thames-festival-launches-with-a-tidal-swim) which was two days after a notification.
If you are tempted by swimming in the Thames then I'd suggest getting some life-guarded pond/dock/lake/reservoir experience and then head to http://tidalthamesswims.co.uk/. That's timed with a turn at slack tide but by the time you get back to the steps to get out the current is remarkable, I can easily see how people that haven't planned the swim and don't know the area can get into trouble.
Is the water quality of the Thames so good you can swim in it everywhere?
Notwithstanding other dangers, of course.
If you swim in the spree inside Berlin you most likely catch something nasty. The sewer system can't retain enough when it rains heavily.
Of course also to do with it flowing so slow.
In summer I really miss Bern and the river Are.