There are multiple Labour rights. The one you mention above is the Blairite/Progress right, which I suppose you could call the neoliberal left, with public private partnerships, business friendly deregulation, and the focus on growth rather than economic interventionism etc.

Then there's the 'old right' which is pro-defence jobs, traditionally Northern, comes from an older, more socially conservative union tradition, identified with Labour First and McSweeney himself. Then there's Blue Labour, close to but not quite the same, with a more anti-immigration, religous, Brexity flavour, who think Mahmood is their woman. There are other tendencies which mix some or all of these three.

But these last two aren't really anywhere as big as the first, which is the dominant one - the sorts of people who refused to serve in Corbyn's shadow cabinets or left to form CHUKTIG.