...quite simply, dogs swimming in this current heatwave is very, very risky indeed due to the increased high risks of them overheating very, very quickly.
As many know part of a humans ventilation is through the skin pores, dogs have no skin pores & only one ventilation system which is through the mouth & nostrils, in this currently warmer water they will heat up very quickly and the risks of them drawing water back into their mouths due to excessive 'gasping type' breathing patterns, the normal human thoughts on dogs in water ''That'll cool him/her down" is totally void in this heat & they can overheat very, very quickly if that happens the dog is as good as dead......
The temprature forecast for the London area tomorrow, Tue, is about 34c, thats about 93-4 Farenheit.

Dogs & overheating

https://www.hillspet.com/dog-care/healthcare/heat-exhaustion-in-dogs
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The link you posted actually recommends swimming dogs.

While I can see doggy pools warming up in this weather I can't see things like rivers getting warm. I know last time I went in the with dog it was bloody cold even in the middle of summer.

The link you posted actually recommends swimming dogs

Yes I know & I agree with them, 'have you noticed' that they are not talking about heatwave conditions? Have you also noticed that I was talking about this current heatwave???
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And again I can't see rivers, ocean, lakes ect warming up to a point it would pose a risk of causing heat stroke. I think it's ott to be worried about it to be honest.

> in this currently warmer water they will heat up very quickly

What people need to be concerned about, humans and dogs, is GREEN ALGIE.   There was an article on TV only a few days ago about this growing with the hot weather and the advice is NOT to let dogs, especially, get into ponds etc. just now.   This can kill.

https://www.gloucestershirelive.co.uk/news/cheltenham-news/warnings-over-harmful-blue-green-1815498

I guess the warning about heat stroke is down to the extra exercise a dog might put out, when swimming = heating up too fast.

http://www.highstreeteppingvetclinic.com/neardrowningsynd.pml was dry drowning more what was being referred to. In this weather the difference in temperature of cold water on a hot body could.make the dog inhale  water more than if the temperatures were more equal. It's also something that can  occur with dogs playing in water  regardless of weather and temperatures having been thrown balls or similar  to catch and inhaling water after doing this afew times

What people need to be concerned about, humans and dogs, is GREEN ALGIE

Yes, thats the worst possible thing to happen and it happens extremely quickly after an intake of the spores, most likely before you and your dog leave area to go home. We even had a main channel warning here (london area) as late on in the year as last week about that killer & Ive never heard or seen warnings so late on the season about it, people don't realize (or take seriously) that the ecological system in an area changes dramatically in prolonged abnormal weather condition changes, every living organism is affected.

As far as Wales is concerned furryfriends see link.

https://bit.ly/2NENIKB
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Now i really am.confused  as to what point  u are making  in regard to dogs that link is of a dried up river due I assume to the weather atm

Blue-green algae, not green   Which are strains of cyanobacteria rather than actual algae.  But yes, it is a serious danger.  The big lake near me currently has a toxic form of it so no humans or dogs allowed near the water.  Some strains can kill within minutes of ingestion.

The local Loch has warning posters when it is around. I was walking down to it one day with my dog who loved water. No posters and a pretty average Scottish summer. He was in front of me he looked back to "ask" if he could go into water and I sent him on. When he got to the edge he stopped and came back. I walked on to look and there was "stuff" which I assume was blue-green algae at the edge.

He always was a clever boy