"...there are hierarchies of laws and rules about what is legal, there are constraints on the powers of parliaments, there are structures for challenge to law makers on, natural law, human rights, constitutionality etc."
No, there really aren't. Actually, of course, there's no need to breach contract law - just introduce a 100% windfall tax on revenues from these contracts. But if Government wants to ride roughshod over the law of contract then it can; might have to leave the EU and the WTO to do it; might face sanctions from the rest of the world, but the Crown-in-Parliament is sovereign and can do anything it likes.
Short of a revolution or military invasion from the outside, of course!
Getting back to the point, in practice, what any new goverment should do is to establish a proper in-house IT operation, refuse to do any big projects for ten years and build up the capacity of the in-house IT so that in ten years' time you can deliver on some of these big projects (the ones that aren't a total waste of time) without needing the consultancies.
Large-scale public-sector IT is different in kind from private-sector IT, and the UK government should recognise this and build up a proper in-house operation, since none of the externals can deliver. Of course, this probably means creating an entire Department from scratch, and I wonder if the Civil Service would settle for having a Permanent Secretary who could write code. Imagine having someone who knew what they were talking about! That would never do!
If you want a big IT project that would really help a lot of people, try integrating the tax and benefits systems into a single one where you tell it how much your earning and your other circumstances (married, living together, kids, child-care costs, housing, etc) and it then did a single calculation to either demand taxes or pay out benefits. Would make everyone's lives a hell of a lot easier, by only having to hand over one set of information to one office, rather than ten different sets to ten different sets of people who then adjust how much you get of benefit A depending on how much you were awarded of benefit B, and then the benefit B people cut that because you got benefit A awarded, so the benefit A people put their amount up to compensate and then you have to pay taxes on your benefits, and then benefit B is increased so you can pay your taxes, but that cuts benefit A and this is about the point that you realise you're a character in a Kafka novel.