The protest, that demanded Brexit to be reversed, took place on Saturday, March 25, 2017.
May has chose to make control over immigration her priority for Brexit and has conceded that Britain must give up its membership of the EU's single market and customs union in order to achieve that.
In addition, more than 60 per cent of its exports go to the bloc and so it would be heavily affected by increased tariffs on its products.
An abrupt exit could "trigger dislocations", with British banks no longer able to offer their services in the European Union and banks in the European Union finding they no longer have access to the financial center in London, the report said.
Over half of Britain's manufactured goods (measured by value) go to the European Union, with manufacturing accounting for roughly 10 percent of the UK's economy.
In the meantime, the fall in the value of the pound has led to a surge in orders, with Britain's factories growing at their fastest pace in more than three years. All three regions backed Brexit.
Mr Barnier said: "While the 27 member states will find it easier to adjust, as they will still benefit from the single market, the customs union and more than 60 trade deals with their worldwide partners, we believe it is in the best interests of both sides to reach a deal on the UK's orderly withdrawal from the EU".
Michel Barnier raised the prospect of long queues of lorries at Dover if customs controls are reintroduced if Britain leaves without a Brexit deal.
London and Northern Ireland are also highly vulnerable if Theresa May fails to obtain access to the European single market at the end of divorce negotiations with EU, the study by think tank Demos concluded.
The EEF urged May to hold a close consultation on Britain's Brexit strategy and said the country should allow a transitional period to ease into its new relationship with the EU.
The Scottish first minister said that Mrs May had accepted in their meeting that the terms of Brexit would be established in time for a referendum according to the SNP's timetable. Manufacturing contributes about 10% share to the Britain's economy.
Loss of access to the single market and the customs union will condemn the United Kingdom manufacturing sector to a painful and costly Brexit, industry body EEF has warned.
But Barnier added an UK-EU deal could be an "ambitious free-trade agreement, provided that it ensures fair competition and guarantees high environmental, social and consumer protection standards".