The prime minister is looking at porn. For research purposes, of course. He's not sitting in cabinet meetings peeking under the table at a looped three-second clip of a woman's bra falling off that Michael Gove e-mailed to him by mistake. He is looking for a way he can pretend to be fighting it. He wants to declare himself the first prime minister to win the war on online porn. And, according to a letter leaked to the BBC last week, he reckons he has found one: default-on.

Default-on is a system whereby internet service providers block access to pornographic images as standard, unless the customer opts out of the filters. In the eyes of certain newspapers, it is the silver bullet solution to the problem of kids watching pornography. But, for various reasons, most of the major ISPs are not up for asking their customers: "Do you want porn with that?" They have negotiated with the government and agreed on a system called "Active Choice +" in which customers opt in for filters, rather than out for falling bras. The system gives new users a choice at installing filters, and existing customers the option of switching to safer browser modes. The default setting remains filter-free.

The leaked letter, sent to leading ISPs from the Department for Education, makes it clear that Cameron's war or porn is propaganda masquerading as policy. It suggests: "Without changing what you will be offering (ie active-choice +), the prime minister would like to be able to refer to your solutions [as] 'default-on'". It is a sleight-of-hand worthy of the Ministry of Truth, a move from the "Let's not and say we did!" school of regulation.

It raises the question: where else does Cameron use this line? Do his aides write to Starbucks, Google and Amazon to ask that, without changing what they are doing (avoiding paying billions in tax), they find a way for him to refer to this as "paying billions in tax"? Do they ask tobacco firms if, without ditching branded packaging, they could find a way for Dave to pretend they have? Has he ever asked George Osborne if he can refer to him as "not George Osborne"?

In a bid to add a veneer of legitimacy to its attempt to call a spade a hosepipe, the letter goes on to ask the ISPs: "Would you be able to commit to including 'default-on' or similar language both in the set-up screen and public messaging?" Which raises the question: how exactly? Ironically? With a winking smiley at the end? By smuggling the words into some irrelevant side-box asking customers "Do you think Greece will 'default on' its debts?" Snuck in as an anagram or across the first letter of each word in a sentence? Maybe it could flash on the screen as a split-second subliminal message?

It almost makes you feel sorry for the internet companies – but their intentions are no more noble than the prime minister's. The ISPs make three arguments against default-on. First, that it encourages parents to be complacent about their children's internet use. Second, that filters are imperfect. Third, that children are smart enough to find their way around filters anyway. All are sound. The third, in particular, is hard to argue with, since any default-on system needs to be simple enough for a stupid adult to navigate, and, if it is, any web-savvy kid should find their way around it in no time. To work, the filters would need to prevent users from asking search engines "How do I turn off these porn filters?" And then the question "How do I turn off the filters for questions about turning off filters?" And so on, for ever.

But I suspect they have their own reason for rejecting default-on, which is that they know if they don't, their call centres will be inundated with bashful customers who have skipped through the set-up process without checking what they ticked or didn't tick and have just realised they are locked out of their favourite porn site. I can hear the calls now: "Yes, hello. I, um, I can't access, er, some of the internet." "Do you mean the porn?" "No, just, er, just some websites." "Porn sites?" "No. Just sites with-" "Porn on?" "Yes, alright, yes. What kind of internet service provider doesn't include the porn as standard?!" It is, in a sense, a fair question.

We – children and adults alike – need to learn about the damaging psychological, social and physical effects of online porn. Default-on would be an error. It would be buck-passing on our part, asking our internet providers to somehow stem the unending tide, rather than face the need for some frank and very un-British conversations. But the worst of all possible worlds is one in which the prime minister announces he has solved the problem when he's only pretending to have brushed it under the carpet.