Only nationalise OpenReach
At first I thought this was a barmy idea but after mulling it over a bit I have grown a bit more sympathetic to it. First of all, a couple of premisses:
1) It is a bit odd that a commercial and independent operator is also responsible for OpenReach where it needs to supply its competitors. There is a reason there have been accusations of market distortion for years.
2) Giving (nearly) every household a 10 mbit pipe is commercially unattractive. There will always be communities where it's just not economically viable if profit is the main motive. Some kind of public sector involvement is required.
3) Having an infrastructure provider as Network Rail in public hands where private operators compete on is a good thing. Whether you agree that Train Operating Companies should be private or public is another matter. I see very few people debate that Network Rail should be privatised too.
Why not replicate the set up for rail similar to that for broadband? Arguably it's even a lot easier than the setup for rail. Therefore:
a) Privatise OpenReach but not BT.
b) Run it with a mild profit aim (but not profit at all costs) for most of the country and then subsidise those areas that would otherwise never be connected.
c) Open the network for all ISPs to offer their services over it with a small profit margin (see b).
The most contentious element is probably this:
If you want free broadband for everyone but don't want to kill the market one could create a (public owned) broadband provider that operates over the OpenReach network at no cost. To keep the market alive it would need be very minimal (max 2Mbit down?). Enough to get access to vital services but not enough to run Netflix, gaming etc.. Anyone who wants a bit more would still need to go to the market and get a commercial subscription.