I'm not sure it's true that Labour's northern support are leave-voters. I mean there's more of them up up there, but in polling Labour voters are something like 65% remain voters. Remember that a lot of the leave vote came from people who previously didn't actually vote - and probably haven't for a while, as general election turnouts have dropped to around upper 60s from the mid 70s over the years.
So although there are a good number of Labour leavers, and they tend to be older and more Northern (and don't forget the Midlands and to a lesser extent Wales) - still most leavers are either Conservative voters or traditional non-voters.
Though it's also true that I think Labour held most of the top ten remain voting constituencies in England in 2015 - as well as most of the top ten leave ones.
I think their real problem is that the voters are still 65% remain, and the members are about 90% remain - but the leadership team are mostly leavers of the Bennite mould.
Though as you say, none of this privatisation can be legal if it reaches the ECJ, with Parliament setting the prices - which would make it pretty awkward to stay in the EU and have these policies.