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As a former Basingstokeite, I second this. But I think Odiham Ford, just down from the canal is reasonably safe, if not particularly deep. My Dad used to take us swimming there as kids anyway.
There's also Longbridge Mill on the A33 between Reading and Basingstoke. There's a great plunge pool bit, out the back of the pub/restaurant of the same name, part of the river Loddon. I'm not 100% sure it's legal to swim there, but it never stopped us as teenagers.
And there's Bourley Lakes between Aldershot and Farnham on the Hampshire/Surrey borderline. It's absolutely beautiful there, it looks like something from the Pacific Northwest. I think it's ex-MOD land though, so it's probably worth checking whether you can swim there.
I have many times but, as you should have concluded by now, I was an idiot in my younger years.
Two I know off. Figheldean and river Nadder by Treffton Elis (spelling on both?).
Otherwise not sure. But I can tell you Basingstoke canal would not be on my list of places to swim!!