All good, but I can see one flaw with bhg's "conversion" in the roofspace with the cold water cistern.
If you cap off the 22mm outlet from the tank in the roof, and connect the pipe run to the mains, then, yes, the sink etc will become mains fed........
................. but, so would the cold feed to the immersion cylinder, and you definitely don't want that. The immersion cylinder would then keep filling indefinitely because there would be nothing to ever stop it.
Occasionally, you find 2 outlets on the roof tank. One for sinks & WCs, and the other for the cylinder. This would be easy, but I doubt if you have that arrangement.