This weekend provided sobering reminders of the human and financial cost of the three-month bombing campaign against Muammar Gaddafi's regime: in Tripoli several civilians appeared to have been killed by a Nato strike; while in London the Treasury chief secretary, Danny Alexander, admitted that the bill for Britain's contribution could run to "hundreds of millions of pounds".

Until now the UK government has shrouded the issue of how much taxpayers are spending on bombing Libya in the sort of secrecy and obfuscation you'd expect if you asked the current location of all its Trident submarines.

By contrast, here are a few things I can tell you about how much the US's contribution to the preposterously named Operation Unified Protector is costing: as of 3 June, Washington had spent $715.9m on its military operation and associated humanitarian assistance, $398.3m on bombs and missiles alone. The Pentagon sent 120,000 halal meals ready to eat (MREs) to Benghazi at a cost of $1.3m. And by 30 September it reckons its Libya bill will have risen to $1.1bn. I know all this because it was laid out in a document produced by the Obama administration for Congress last week.

On Friday I tried to find out some equivalent figures for Britain's involvement. I called the Ministry of Defence, where a spokeswoman told me the Treasury was "doing an assessment", but no "actual figures" were available yet. She mentioned a month-old estimate "sort of within the region of £100m", but conceded that since the deployment of Apache helicopters the figure was probably significantly higher.

She thought the Treasury might be able to provide more detail, which did not amuse the Treasury spokesman I reached: "It is currently not possible to pull together real-time figures. Apparently the MoD are working on a breakdown but that's not ready to be released."

Perhaps the Foreign Office could help? Not likely: "The foreign secretary has made clear that we will present accurate costings to parliament in due course. We will not be providing a running commentary."

This from the government that trumpets its commitment on the Downing Street website to being "the most open and transparent in the world".

Fortunately, we do know a little more about the likely bill for Britain's part in the conflict from other sources. This month Nick Harvey, the armed forces minister, said in answer to a parliamentary question that Britain was targeting Libya with £6m worth of munitions a week. A Guardian report in May quoted defence experts who suggested the total bill by autumn is likely to be £400m-£1bn.

Public spending comparisons can be glib, but in times of slashed budgets and brutal choices it is hard – perhaps even irresponsible – to avoid making them. So here are a few striking ones: taking the most conservative estimate, the cost to the UK taxpayer of bombing Gaddafi for six months is four times the cut to the arts budget; three times the sum saved by Ken Clark's controversial sentencing reforms; more than the proposed cuts to the legal aid budget; about the same as the savings from ending the education maintenance allowance (EMA); or three times the amount saved by scrapping the disability living allowance.

Are these reasons to conclude Britain should stop bombing Gaddafi? Of course not: any decision to go to war is a complex equation of morality, risk and national interest, in which financial cost is just one, frequently trumped, consideration. But are they relevant to forming an intelligent view on whether Britain should be involved? Surely.

Yet when it comes to military action there is a curious reluctance to apply the same scrutiny to the bottom line as we do to every other area of public spending. As the New Yorker's Amy Davidson puts it: "There is something almost pathological about the way we don't talk about budgets when we talk about war … as if brave men don't think about things like money."

Anyone who has the temerity to ask how much Britain's Libya campaign is costing is reassured that it is all being paid for from Treasury reserves, so we needn't worry our pretty little heads. But anyone who has lost their EMA or disability living allowance could quite justifiably wonder why cash can be found for bombs but not for them.

At the very least, a democracy ought to ventilate the choices it is making. Ed Miliband has been reluctant to rock the boat over Libya, perhaps because the Labour leader can see no better option. But it's time his party started asking difficult questions about our third war in a decade. And if David Cameron is serious about transparency, he needs to show he can be as open about inconvenient facts as he has been about inconsequential ones.