"Labor is pro-remain, right?"
No. Labour is pro-will of the people on Brexit, with the caveat that the people should be properly and fully informed of the consequences before they make a decision and thus should have the right to change their minds if they were not. Despite its many benefits the EU is a shamelessly neoliberal organisation, so Labour won't shed too many tears if we do leave as long as the country isn't harmed in the process.
So far as EU regulations go, they of course won't apply if we do leave the EU. However, we may not yet leave. If we do remain, the important thing to note about that regulation is that it says state intervention should be limited *as much as possible*. If the free market and commercial investment were both interested in providing a full national fibre network and able to do so, even paid for by the user, they've had plenty of time to do it. It seems reasonably obvious that if the State wants to achieve the goal of 100% fibre broadband coverage, it's going to have to do it itself.
Lastly: in this modern era the data network should be considered an essential part of national infrastructure. As such it is too important to be privately controlled.