And let's not forget that it's basically a basic necessity to have "full-fibre broadband" connection today, really no different from having access to running water. According to Labour, British pupils apparently can't even do their homework because their crappy ADSL is just too slow.
Also, let's not confuse "free high-speed broadband to every residence in the UK" (which, by the way, is a ludicrous proposal which could and would never work*) with a universal service obligation (USO).
BT had - and still IIRC has - a USO to provide a wired telephony connection to every residence in the UK that requests it, whether that residence is in Guildford or in the remotest corner of the Outer Hebrides. And if a residence has a wired telephony connection, it can get ADSL broadband. Now it may be that in extremely remote location, ADSL might only run at 2-4Mbps, and that's certainly a problem when it comes to things like live video streaming. But it's more than enough to allow for multiple simultaneous users viewing text/photo web pages, sending emails, or downloading video files.
The UK is, in fact, already in the process of collaborative funding (central government, local government and BT) to extend faster fibre-to-the-kerb (FTTK) broadband to remote parts of the UK, in a scheme known as Broadband Delivery UK. This is an ongoing project, and should result in the vast majority of UK residences being able to receive broadband at up to around 20Mbps.
But the crucial point to remember is that this is only about the provision of higher-speed broadband. It's absolultely not about "free high-speed broadband". People in extremely remote areas will almost-certainly still be required to pay an additional set-up fee to contribute to the cost of running cable to their vicinity. And there will still be a payment mechanism for everyone who takes broadband, which will cover expenses associate with initial setup, the running of the network, and an implicit contribution towards the construction of the network. There cannot and will not ever be "free high-speed broadband".
* Firstlyi f a Labour government really did want to renationalise Openreach, it would cost them upwards of £20 billion (and their proposed UK budget doesn't come close to fiscal balance as it is...). And even then, they haven't apparently addressed the difference between network infrastructure and operation of services over that infrastructure. The very reason why Openreach was separated from BT was to allow for transparency: BT now offers internet services over the Openreach network - and pays an onward charge to Openreach for the use of that network - in exactly the same way as many other internet service providers (eg Sky, TalkTalk, PlusNet) offer services over the Openreach network and pay Openreach for the use of that network. There is no way whatsoever that a Labour government could hand out free broadband: not only would it have to create its own internet service provider, but it would also face humungous restraint-of-trade lawsuits from all those other ISPs. It's not going to happen. Period.
