As is partly evident from this article it is not practical. There have been several attempts to do the hydraulic modelling and they have all come to naught. That map was constructed in the 1970s, in the pre privatisation, isn't that a pie up there in the sky, era. (even engineers have dreams)
There are hills in the way. There is no handy downhill sloping route from Cumbria to the Thames basin. Even if there was, it would be covered in cities, factories, roads etc.
Even if it was feasible it would be a vast expense. Would make HS2 look like peanuts. The government isn't going to shell out (not their problem - its been privatised) and who would pay - the water company that is maybe going to sell its water to another water company? (they could not afford to borrow the many billions required with no return on investment for a long long time) or Thames water, at the other end of the pipe? Ultimately it would push someone's water bills sky high. And take a decade or two to accomplish - planning permission alone would be mind boggling.
So you have a daft idea being aired (yet again) just to create a news article.