No Heath and the liberals would just not have a referendum because they are in power. Most center left leaders would support a referendum but would be neutral and not officially campaign for leave but shore would campaign hard
I wasn't saying that Heath would hav a referendum, but that Labour would have one upon returning to power under Callaghan or someone, before Shore would have a chance to become leader, if he ever did.
If this leads to Labour, rather than the Conservatives, reaping the benefits of the late '70s/early '80s economic turmoil, would Britain have perhaps dodged neoliberalism to a greater extent than most Western countries? Or would the government have ended up going the route of Hawke/Keating Australian Labor or Lange/Douglas New Zealand Labour?
Maybe. There would still probably need to some form of monetarist reforms (as was already happening under Callaghan), but I'd imagine that Labour would also keep the trade unions fairly strong as well. Perhaps it would be more like France than Australia or NZ. Alternatively, Labour fails to get to grip with any of it, and is kicked out of office after five years.
Well in this timeline Callaghan I think Callaghan would plan to resign in 1982, but due to the Falklands war he stays to finish that off. He would succeed as he was not unused to sending in the army to deal with others, for example in Northern Ireland in our timeline. This then would lead to a patriotic boom, like in our timeline, and Callaghan would call a 1983 election, to bank off this boost in popularity. But at this point he would be 71 so he would resign soon after the election and labour leadership election between members like Peter Shore or Denis Healey (in my opinion the two biggest players, maybe Tony Benn)
Shore was disadvantaged by not being strongly identified with the left. If someone with stronger Bevanite credentials, such as Foot and Kinnock came forward, then they would probably take him out of the top two. He'd only win if the left had nowhere else to go, and Healy ran as a poor a campaign he did IOTL, which me might not especially if someone like Hattersley ran on a platform that was more firmly anti-left.
Also, the Falklands very likely wouldn't happen in this situation. Even if the Heath-Thorpe coalition didn't butterfly it away, the consensus seems to be that Labour would have maintained a stronger RN presence there in the run up to war (which Thatcher withdrew IOTL) and therefore would have deterred Argentina from ever invading in the first place.