The Chairman of the European Research Group (ERG) said the UK is willing to move forward with Brexit “with or without them”.
He wrote in the Sunday Telegraph: “We are told trade won’t be possible unless we stay within the regulatory and legal order of the EU. Four times the British people have voted recently not to do that.”
Mr Baker, who was previously given the moniker “rebel commander”, added he hopes sense will prevail in the negotiations but “sense hasn’t prevailed in the past and looks at risk today”.
Nearly four years after the historic referendum, the UK will leave the EU on Friday.
The Government will then have one year to negotiate the country’s future relationship with the EU.
Mr Baker wrote: “Today our impatient, well-meaning friends in the Commission are making dread threats of non-cooperation and domination.
“Despite agreeing to negotiate the future relationship this year, now they say it will take too long.
“The UK has now decided who we are and what we wish to become: a free and responsible people achieving great things with our friends.
“We must hope our friends make allowances and walk with us, for we will now go where we have agreed, with or without them.”
He argued threats from the EU will prove futile with the country willing to go it alone if there is no cooperation reaching a deal.
He highlighted previous attempts by Prime Minister David Cameron to renegotiate the UK’s relationship with the European Union.
“The public asked for change and the powers that be refused,” he said.
Mr Baker chairs pro-Brexit group the ERG, who have lobbied the government over the UK’s withdrawal from the EU. He took over from predecessor, Jacob Rees-Mogg in September last year.
He has previously accused anti-Brexit campaigners of continuous scaremongering regarding a drop in standards in post-Brexit trade deals with other nations.
The Tory MP insisted the UK will remain a “high standards nation” on the global stage.
However, Ireland has refused to rule out vetoing a Brexit trade deal that splits from EU rules.
The Irish Europe Minister has also hinted there could be further delays to the negotiations, despite the Prime Minister’s insistence on a 2020 deadline.
In a sign that trade talks could quickly become deadlocked, Helen McEntee told Sky News that the level of divergence proposed by the British government was “worrying” to the EU.
She repeatedly said the focus should be on getting a “good deal”, not just the timing.