That's bollocks, for most of the country speeds are determined by whatever technology BT decides to give them. The competition pretty much decides who send you bills and who you shout at when it doesn't work.
This simply isn't true, unbundled providers exist pretty much everwhere in the country and have their own equipment in the cabinet. Sure, open reach provides the back haul, which is why that's crap, and open reach provide the wire, which is why that's not been replaced since the early 1900s.
Corbyn's plan is to take out the one bit that open reach haven't fucked up.
If you have a bad line, then get your arse together and pull the bloody thing down so they run a fresh one. That's how you used to get stuff done in the state monopoly days, because none of the employess gave a toss.