That was the promise made by the Prime Minister at the weekend. But it left open a number of questions - did he mean everyone, no matter how remote, what technology will be used, and who is going to pay for it?
Here is what David Cameron said: "Just as our forebears effectively brought gas, electricity and water to all, we're going to bring fast broadband to every home and business that wants it."
As the government has already promised to bring fast broadband to 95% of homes via the BDUK programme, this is all about reaching the final 5%.
The digital minister Ed Vaizey gave further detail, explaining that the plan was to bring in a universal service obligation of 10Mbps for "the very hardest to reach homes and businesses."
But does that mean every home - even those up Welsh mountains or on remote Scottish islands?
Let's presume it does, though just as with the obligation on BT to provide a phone line, there may be some upper limit on the costs involved in hooking up a home.
Broadband campaigners have not greeted the government's pledge with huge enthusiasm.
In particular, they have derided that 10Mbps minimum as woefully inadequate.
I contacted a number of them to ask what the minimum speed should be and got answers ranging from 15Mbps to 100Mbps.
There was also general agreement that fibre to the home was the technology which should be employed, though a few pointed out that 4G was now providing better speeds in some areas than fixed line broadband.
The problem is that, even at a minimum 10Mbps, a universal service may prove an expensive undertaking and the cost of putting a 100Mbps fibre connection in every corner of the UK could be prohibitive.
When the debate about fast broadband got going, it was calculated that universal coverage might cost at least Â£15 billion.
A  government which is implementing severe cuts in public spending will not be keen to put more money into broadband - although of course it is worth remembering that most of the cash spent so far on the BDUK programme has come from the TV licence fee.
And just about all of that spending has been channelled through BT, which was the only company to apply for the money in most regions.
Now the former monopoly telephone supplier looks likely to be a the centre of the effort to hook up the last 5%.
But even if the government wanted to spend taxpayer funds to make that happen, there will be resistance from BT's rivals.
Virgin Media has already called for an end to subsidies for rural broadband, claiming the market can now do the job - although it isn't clear that it will be moving to offer cable to every remote home.
Meanwhile, there are signs of a split opening up between town and country over the subsidy issue.
The director of the free market Institute of Economic Affairs Mark Littlewood told Radio 4's PM that people living in remote rural areas had made that choice, and fast broadband should not be a right.
Rural broadband campaigners hit back.
John  Popham, who advises rural communities wanting to get connected, told me there was already a widening gap between town and country: "For me the issue is that urban connections are getting faster. Stuff is then developed to take advantage of those fast connections which is then inaccessible to rural users."
Many of those campaigners have been deeply sceptical about BT's strategy for rolling out fast broadband, and some have joined calls for its Openreach division, which operates the fibre and copper networks, to be sold off.
But here's the paradox - the move to make fast broadband a right for everyone could end up strengthening BT's hand. If it is asked to meet a Universal Service Obligation, without being offered subsidies to make that feasible, then the company will want something in return.
It is Ofcom, not ministers, which is currently pondering whether Openreach should be sold off.
But the regulator will be hearing strong arguments that a divided BT will not be in good shape to help the Prime Minister fulfil his promises on fast broadband.
So, every home and business across the UK can now have fast broadband if they want it.