If you read the original piece, it's clear that the author sees the Constitution as a bulwark for government programs (education, healthcare, politics of race, etc.) rather than against government abuses. I'm suspecting the same "logic" is at work in Britain; a decade of Blairism has led to many changes in British state and society, and it's only natural for Blair's heir to wish to cement these impositions, rather than risk them undone by someone else down the line.
Here's a passage from the NZ Herald op-ed that seeks to camouflage this sentiment and present a constitution as a protection of rights:
The Institute for Public Policy in Britain has warned that its Parliament can deprive citizens of centuries-old rights "by the same means as an alteration of the speed limit" - that is, a 51 per cent vote.Welcome to democracy! That's precisely what it's about, when one gets rid of the legalistic frills. Of course the thought is terrifying. But it is precisely because the Parliament has such power that it has been exercised with restraint. That is, until Oliver Cromwell Blair chose to remake Britain in his own vision...
The American constitution, which established the federal government of the U.S.A., was a compromise between statist, empire-building ambitions and a conservative distrust of government. Fast-forward 200+ years since its passage, and one can easily see all the provisions limiting federal government power either circumvented or ignored completely, while a multi-trillion-dollar bureaucracy employing millions has arisen out of deliberate misinterpretation of a couple of words (i.e. commerce clause). But Americans today insist they are free, because the Constitution protects them. Right. And the Moon is made of cheese.
States love constitutions. Rather than being the chain that binds their power, constitutions are a disguise that protects their tyranny. When the behavior of the state is governed by tradition, history and precedents, society has control over the state. Once a paper replaces tradition, that control moves into the hands of the state itself. A court reviews it, a parliament of some kind amends it. The state becomes its own arbiter. How likely is it to judge itself harshly? If you answer "very," I've some beachfront real-estate in Nevada for you. Call now, operators are standing by.
If Britain gets a constitution - and with Labour controlling all the levers of government, the question is not "if " but rather "when" - it will become even less free than it is today (which, admittedly, isn't much). I don't know how highly the Kiwis value their liberty, but they are guaranteed to lose it if they follow Britain's example; leaving Israel as the only democratic state that answers to an authority higher than itself.
Aptly ironic, if you ask me.