It's easy to see how that might be beneficial for Internet: pay Openreach for last mile access but your chosen operator takes over after that. You can see an advantage for electricity and gas if you squint really hard: your supplier is responsible for buying power to add to the grid to serve you, and different suppliers can make different (if heavily constrained) choices.

It's really hard to see how this works with water. Upstream of your taps is an essentially fixed set of water collecting infrastructure. Downstream of your waste pipe is a natural monopoly sewer system which collects waste towards a single geographically determined water treatment plant. What is there for a competitive operator to change?

The honest answer is that water privatisation was the product of a very specific brand of 80s-00s magical thinking that believed the private sector was necessarily more efficient even without a plausible model of how the efficiencies would happen. There's a reason water and rail were two of the last privatisations, long after all the things like British Airways where there were reasonable grounds to believe the private sector was a better home.