As far as I know there is no secretive government agency that keeps a trio of strange, other-worldly teenagers in a water pool, wires attached to their brains, exploiting their eerie ability to see into the future. But, that detail aside, the 2002 film Minority Report can claim – like the "precogs" in the pool – to have predicted the future with uncanny accuracy.

The film depicted a mid-21st-century world of robotics and assorted gadgetry, with a few striking specifics. The first was the way Tom Cruise and friends used computers. No laborious typing on keyboards, just swishing and swiping with their fingers. Well, that future didn't take long to arrive. Thanks to Steve Jobs and his touchscreen gizmos, Minority Report-style hand movements are already here (even if we are still lumbered with actual screens, rather than the film's holographic images hovering in the air).

Cruise was seen walking past posters that moved, screens that showed short, silent advertisements. Tube stations and even some bus stops now have those too. But in the film the ads recognised Cruise and addressed him directly. That seemed both sinister and unlikely in 2002. But this week we took another step towards it, thanks to that all-pervasive presence in our lives: Google.

On Thursday, Google took down the barrier that had, until now, prevented it joining the dots of your electronic life. It had already been logging all your Google searches, remembering what you looked for and when, as well as watching what you watched on YouTube, photographing your house for Street View and, if you use a Google smartphone, knowing where you've been and maybe where you are right now. It had been using that information to generate, to take one example, the ads that appear on your Google search page based on your past searches. But it had never connected these separate silos of information.

Now it will. Thanks to a change in its privacy policy, Google can make deductions based on one aspect of your online activity and use that to sell you things in another. If you watched football clips on YouTube, an ad for upcoming matches might appear beside your inbox. Perhaps that will strike you as efficient rather than sinister, but consider this: if you use a Google email service, then Google will be reading your emails too. It's true there is no human pair of eyeballs gazing at your daily correspondence: the "reading" is of the electronic, algorithmic variety. But it will be just enough, as my colleague James Ball put it this week, that if you sent an email to a friend announcing "I'm pregnant!", your next browsing experience could well be interrupted by ads for maternity wear. Just like Minority Report imagined it.

Perhaps Hollywood thrillers are not the best guide to what's scary and what's safe. Maybe we shouldn't shudder at the warning that when an online service is free, you're not the customer – you're the product, a valuable source of data ripe for commercial exploitation. It's possible that this sounds creepier than it is. Perhaps all this knowledge held in Google's vaults of humming, blinking servers will only ever be used to help us go shopping or find a decent restaurant.

But there are other possibilities. What if some of that information leaked or got lost? What if Google chucked out a few old servers containing millions of our emails, in just the same way that the last government managed to lose the personal details of 25 million British citizens? Google now holds so much data that industry watchers assume it is a target for state espionage; assume indeed that every self-respecting intelligence agency in the world is trying "to get an engineer into the Google server room". The company has accused China of attempting to hack its Gmail service, trying to read the emails of US officials and Chinese dissidents.

It should give us pause, too, that if the US government wanted to subpoena emails between, say, a journalist and a confidential source, Google could, if it chose, simply hand over those emails without even telling those involved. The power lies with Google, not the people who sent or received the messages. And power is the right word. If knowledge is power, then Google is a global superpower, the match of any government. It doesn't raise armies or levy taxes, but its reach and influence are enormous – and getting bigger. The trouble is, our political vocabulary does not quite know how to speak about this kind of power.

Our institutions, our rules of engagement, were devised for the age when governments were the only force with sufficient clout to be feared. In America, the constitution is all about holding in check the threat of over-mighty government. In Britain, we act as if politicians were the sole wielders of serious power – interrogating them on the Today programme and Newsnight, endlessly examining their words in the newspapers. And yet, today, government is just one of the forces capable of shaping our lives or threatening our liberties. Yes, the Department of Health holds your medical records, but Google has almost everything else. If you worry about one, shouldn't you worry about the other?

Many will say they clocked this point long ago, speaking about corporate power and the like. But that won't do. Acknowledging the might of "the multinationals" is too abstract. Instead, we ought to recognise the muscle of specific companies, invigilating them, holding them to account as surely we would any government ministry.

Google would be one candidate for this treatment, and after this week we could all name another. When the Met's Sue Akers told the Leveson inquiry that News International had built a "network of corrupt officials", with paid informants in the "police, military, health [service] and government", the notion of a Murdoch-run shadow intelligence operation, watching the people of this country, monitoring anybody who stumbled, even through tragedy, into the public eye, no longer seemed so hyperbolic.

We are not powerless in the face of these threats. The greatest challenge to Google, as it was to Microsoft and its monopolistic practices, might well end up being the unloved EU. But the first step is to recognise that the power exercised in Westminster is far from the only one that counts. To know that, you don't have to be able to see into the future – just into the present.

Twitter: @j_freedland

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