It’s almost a decade since David Cameron scrapped Labour plans for a national ID card, and 13 years since fears about the government tracking all our movements helped kill off pay-as-you-go road pricing.

The idea of a “black box” in the car, logging every mile driven, was deemed too creepy, even though in hindsight it could have lowered carbon emissions years ago by discouraging drivers from making unnecessary trips. But Britons guard their privacy jealously, at least outside wartime. It’s surprising, then, how little debate there has been about the electronic surveillance culture this epidemic threatens to bring with it.

This isn’t about police sending up drones to shame Peak District ramblers, or threatening to snoop through supermarket shoppers’ trolleys to check their trips were really necessary, but about what happens after lockdown is over. Matt Hancock, the health secretary, confirmed at the weekend that the government is seeking to develop a phone app allowing people to record their own symptoms, and receive alerts if other users they’ve been in contact with have fallen ill. Well, of course he did: this is the man who once invented the Matt Hancock app, for everyone desperate to keep up with all the Matt Hancock news. But what if this is more about Matt Hancock keeping up with you?

Any future tracing app would almost certainly be voluntary in Britain, with strict confidentiality promised to protect users’ privacy. It could be a godsend for people with vulnerable relatives, giving early warning of any brush with the virus that would help them to avoid unwittingly passing it on. True, we’d be meekly handing over intimate details of our movements and social circles to an alliance of government and tech companies, but arguably that’s no more information than we blithely give away by opening Google Maps or Facebook. Like staying home to save lives, getting the app could become seen as the socially responsible thing to do, helping save jobs by allowing a gradual return to normal while lowering the risk of reigniting infection. But, given that this could be a far longer lasting change to everyday life than lockdown, it’s staggering how little we have been prepared for it.

In authoritarian states such as Russia or China, the fear is surely that tracking systems could be abused. When Chinese citizens with a green code (for low infection risk) can go out, while a yellow or red code (denoting contact with an infected person, or confirmed infections) means restrictions, how easy would it be to punish political dissidents by tampering with their codes to keep them under effective house arrest?

In Britain, the worry is more that everyday life could swiftly become difficult for those unwilling to sign up. Even if it’s strictly voluntary, are we so sure that unscrupulous employers wouldn’t demand applicants install the app as a condition of hiring, that rogue landlords won’t try to discriminate against tenants who can’t show they have it, that insurers won’t seek to restrict health cover accordingly? Could airlines insist you get it before you fly, to protect fellow passengers? The risk is of creating another kind of hostile environment for those who resist. And that’s to say nothing of questions about what access the security services might eventually seek to the data, or whether electronic tracking could become a habit that sticks once the epidemic is over. (Maybe road pricing isn’t so dead after all.)

It’s easy to see why government doesn’t want to have this conversation now, arguing that talk of exit strategies risks distracting from core messages about staying home. Although Dominic Raab is expected to announce on Thursday that lockdown won’t be lifted until after 7 May, that’s simply the earliest date for review; there’s no guarantee it won’t drag on longer.

Yet the implications of something like this need to be thoroughly explored before we move from blanket lockdown into what could be a more fluid and personalised version, where we might get something like our lives back but have to live with knowing they could be snatched away again. Ironically, it’s probably those libertarians howling loudest for an end to lockdown now who’d naturally hate the idea, while for others it will sound like a price worth paying for escape. Right now, I’d probably download it like a shot. But until some basic questions are answered, we just don’t know what we might be sacrificing for freedom.

• Gaby Hinsliff is a Guardian columnist