Update, as we've been away on a hiking trip and in the meantime some changes were introduced in our home

The tub which I linked to in the original post turned out to be not suitable. When I phoned to purchase it the company were very helpful, and they explained that the tub could only be filled half-way up, due to not very strong plastic it is made of (if it is filled more, the sides would begin to bow out).
So that idea had to be scrapped, but I already knew what I was looking for - a Japanese deep bathtub. In our house the garage adjoining the house is converted to make a dogs' bedroom, and there is a utility space next to it where we've had a small bathtub installed for washing the dogs after walks and similar things. So we decided to replace it with the Japanese version, which suited the available space perfectly as these baths are relatively small but very deep.
While we were away the tub was delivered and installed, and we have swam our four beasts in it already. It absolutely works, our dogs each had about 5 minutes of swimming session (to start with as it was their first) using the harness and me supporting the dog in the middle of the bathtub. The dogs seem quite happy about it once they realised it was for fun (nicely warm water and using their favourite toys helped).
Once we swam the first dog though it became clear that my earlier thought of "putting a tub in the middle of one's living room" was not a very good idea, as there were splashes and splashes of water all around. Therefore utility room with moppable floor or similar is necessary.
Overall I couldn't be happier as this turned out to be the perfect solution to introduce a swimming exercise for our dogs every now and then, and in all weathers