Former trade minister and ex-CBI chief Lord Jones of Birmingham, Leave Means Leave co-chairman John Longworth and Labour Leave chairman John Mills were all due to meet Mr Barnier in Brussels.
Mr Longworth, a former director general of the British Chambers of Commerce, said he would tell Mr Barnier that any post-Brexit trade deal must not restrict the UK’s “economic and regulatory freedom”.
He said he would tell the Brussels official that unless progress on a deal is made by the middle of the year, the UK could walk away from talks and revert to World Trade Organisation rules.
He said: “I will use this opportunity to make it clear to Mr Barnier that the British people will not exchange their newly won freedoms for a trade deal with the EU.
“Crucially, this means that the UK will have the economic and regulatory freedom for our businesses to thrive.
“The EU must accept that in the event that a transition period is required, it will be both limited in its coverage and fixed in its length and an FTA (free trade agreement) must be agreed before the transition begins.
“The speed at which negotiations are taking place must be intensified.
“If the heads of terms on the FTA are not agreed by mid-2018, the UK Government will have no option but to postpone any trade negotiations and revert instead to global rules of trade under WTO in order to provide assurance and stability to British businesses.
“I have no doubt that Britain will thrive with or without a trade arrangement with the EU so long as the Government leverage our newly won economic freedoms.”
Lord Jones said trade negotiations “are always about reducing tariffs and not increasing them”.
“With this one, we’re starting at zero and that is where they should stay,” he said.
John Longworth said he would tell Mr Barnier that any post-Brexit trade deal must not restrict the UK’s ‘economic and regulatory freedom’ (Ben Birchall/PA)
“We should also start serious discussions about bureaucratically obstructive and delaying non-tariff barriers to trade.”
Mr Mills said: “It must be made clear to Barnier that the possibility of the UK staying in the single market is simply not an option.
“It wouldn’t give the UK control over its borders or judicial system, and is not what the British people voted for.
“Instead, we need to focus all our energy on reaching a deal that is beneficial for both the UK and Europe.
“If that is not possible, the UK can safely fall back on WTO terms and we need to make that option clear.”
The meeting was brokered by independent MEP Steven Woolfe, a former Ukip member, and comes after Nigel Farage held talks with Mr Barnier on Monday.
The pro-Brexit delegation presented Mr Barnier with a hamper containing UK produce including wine and gin, Marmite, PG Tips tea, the complete works of William Shakespeare and a biography of Sir Winston Churchill.
After Mr Woolfe posted photos of the “fantastic products from Britain” on Twitter, other users were swift to point out that Marmite and PG Tips are produced by the Anglo-Dutch group Unilever.
He responded: “Precisely. To show we want the UK to retain close ties with our EU friends.