At a guess, I would hazard the thousands of people who would become unemployed? And not all be able to immediately go and work for the 'British Broadband Corporation'? That's one negative side effect.
So we should have worse, more expensive internet instead, to keep people in positions that aren't necessary? That seems like a terrible idea. Presumably a Labour Manifesto with this policy in it, would also include a bunch of provisions for unemployed people.
Presumably taxing people more to support them? I don't have a dog in this fight. But probably wise not to infer there aren't negative consequences if all bar one broadband companies get shuttered in a country.
I would gladly vote for paying all employees of all ISPs their current salary from taxes for a while, if it meant free, nationalized fast fiber in every home.