"Let me be clear, compared with today's smooth single market, all the likely Brexit scenarios will have costs for the economy and to a lesser extent as well for the EU", Lagarde said as the International Monetary Fund presented its annual report on Britain's economy.
In a letter to EU leaders he said they should discuss arrangements for the "final phase" of the Brexit talks "including the possibility of calling another European Council in November".
Presenting a report on the UK economy to the UK Treasury on Monday, IMF managing director Christine Lagarde said: "Any Brexit deal will not be as good as the current smooth process by which goods, people and services move now".
Despite Barnier's upbeat mood, there is, so far, no full exit agreement and some rebels in British Prime Minister Theresa May's Conservative Party have threatened to vote down a deal if she clinches one with the EU.
He added: "We're urging the Government to concentrate on getting a deal to ensure the continuation of tariff and friction free trade which is so important to the future of our economy".
Gove's intervention came hours before former Cabinet colleague Boris Johnson launched yet another broadside against the proposals, suggesting that ministers had been misled about the implications of the Irish backstop agreement.
Michel Barnier will deliver an update on the remaining issues that need to be resolved in the divorce talks - including the Irish border question, and the framework for the UK's future relationship with the EU.
If an agreement is reached, Britain and the European Union have said that people will continue to be able to move, live and work on the same basis as now up until the end of a transition period in December 2020.
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United Kingdom customs officers would charge different tariffs at the borders for goods bound for the domestic or European markets.
He reiterated he was equally keen to prevent a hard border between Northern Ireland and Scotland as between Northern Ireland and the Republic.
Arriving at the Brussels meeting, Brexit minister Lord Callanan said: "If we are to get a deal there has to be compromises from both sides and we look forward to seeing what the European Union side has to say about this".
Theresa May must consider alternatives to her Chequers blueprint that keep Britain aligned to Brussels to avoid a "chaotic and damaging" no-deal Brexit if it is rejected, MPs have warned.
"There are potentially two approaches: have a joint political declaration which is very much clear to the last point or to have a political declaration which while registering an agreement on a number of issues, leaves a certain space for negotiations in the future on a number of issues". But I don't think it's in anyone's interest for that to happen.
Gina Miller, the financier who took the government to the High Court, and is fronting the campaign for a second "People's vote" on the outcome of the Article 50 negotiations, was the main speaker.
"I don't want manufacturers to feel that they've got to operate under all sorts of different rules, because that complicates life for them and that potentially means business leaving this country", she said.