He urged David Cameron "to end the pretence" of EU renegotiation and back an "out" vote at the referendum.
Dr Fox also said cabinet members should be able to campaign for an EU exit without having to resign - despite disagreeing with the prime minister.
But former Tory prime minister Sir John Major said it would be "extraordinary" if ministers chose to break ranks now.
Mr Cameron has promised to hold an in-out referendum on EU membership before the end of 2017.
The prime minister said on Friday the UK would "fundamentally change" its relationship with the EU in 2016, following talks with fellow leaders in Brussels.
But Eurosceptics say his demands are trivial and will not have any impact on levels of migration to the UK from elsewhere in Europe.
What does Britain want from Europe?
Cameron hints at 2016 referendum
Dr Fox told the Sunday Times the sight of Mr Cameron taking "the political begging bowl around European capitals" to secure only minor reforms should be enough to persuade people to back a "Brexit".
He also told the BBC's Andrew Marr show the recent decision to create a single EU-wide border force was a critical moment.
"This is a force that will be deployed by the [European] Commission, not by elected governments, and in fact, can be done against the will of sovereign governments.
"That for me is the clearest possible indication about the direction of travel of Europe and I can't accept that."
According to reports in several newspapers, some senior ministers are prepared to resign if they are not allowed to campaign to leave from inside the cabinet.
Dr Fox said individuals should be able "to express what's effectively a matter of conscience for them" without resigning.
"I think that the more that we're able to give freedom to our colleagues and treat one another's views with respect, the easier I think it will be for us to come together after that referendum to continue to govern to country."
But Sir John told the BBC it would be extraordinary if anybody decided to campaign against cabinet policy - at least until Mr Cameron had completed his negotiations.
"I would hope afterwards that they would not wish to, because the unity of the argument for the sake of the country is very important," he continued.
"This is bigger than the Conservative Party. People deserve to hear a clear-cut argument, not an internecine piece of party strife."
Steve Baker MP - co-chairman of campaign group Conservatives for Britain, which wants far-reaching EU reform - told Sky News there would be "something of a pantomime for several months" if ministers were forced to toe the line.
"I think it is inevitable that some members of the cabinet will feel they have to resign if they are browbeaten into supporting a deal this flimsy."
But pro-European former minister Ken Clarke told Sky News it was perfectly possible for different branches of the Conservative Party to have a "sensible" and "rational" debate.
"Euroscepticism is, I think, a euphemism for right-wing nationalism, but that doesn't mean I don't think that some of them are quite intelligent and sensible and perfectly nice right-wing nationalists."
Mr Cameron is demanding change on four issues, including stopping migrants from the EU from receiving in-work benefits in the UK until they have been in the country for four years.
Sir John said the renegotiation "embraces many of the things" Eurosceptics have long campaigned for, so it was "essentially bogus" to argue that the reforms were trivial.
He also questioned whether opting out of the EU would help reduce immigration.
"If we had control of our own borders I wonder what would happen to all the people who had got into Calais.
"Would the French keep them there, or would they say, 'This is no longer our problem?"
Sir John said it was "a fantasy" to believe the UK could become "a closed nation".
"Of course we will survive [if we leave]... the point is, would we be as safe? No. Would we be as well off? No. Would we be as influential? No."
There are currently two campaigns advocating exit: Leave.EU and Vote Leave.
Dr Fox said they must speak with a united voice and he would happily share a platform with UKIP leader Nigel Farage.
"I think it has to become a question of the issue and not a question of personalities."
Q&A: What Britain wants from Europe
Guide to the UK's planned in-out EU referendum
BBC News EU referendum special report
Conservative former defence secretary Liam Fox has said he will vote for the UK to leave the European Union.