Carolyn Fairbairn, director general of the business organisation, will stress that urgent progress is needed on agreeing a transitional deal with the EU by the end of March and the framework for the future trading relationship with Brussels must be set out by October.
Businesses are “deeply apprehensive” about the current uncertainty and there has been “too much ideology, too little urgency” in the negotiations, she will say in a speech on Monday.
The Prime Minister has ruled out remaining in the single market and customs union after Brexit and is seeking a bespoke deal to preserve as many of the benefits of EU membership as possible while allowing the UK to control its borders and strike trade deals around the world.
The EU has indicated that the only options available are a Canada-style trade deal, which may not allow the UK the same level of access for economically important service industries, or Norway-style single market membership which would entail continued free movement and payments to Brussels.
The CBI leader will use her speech to say neither option is right for Britain and both sides should think again.
The Canadian model's “rules of origin are as long as The Lion, The Witch And The Wardrobe - and a lot less fun to read” and such a deal is “an ocean away from what we need”, she will say.
The Norwegian model is better for business but its “lower level of control is a problem” - it would be politically difficult for Mrs May to accept a situation where free movement continued and payments were made to EU countries.
The negotiators should adopt a flexible approach of starting with the rules that are already shared and moving on from there, she will say.
Most businesses with supply chains crossing the EU will want to maintain current arrangements but in other areas there could be divergence.
“We know future divergence might come at the expense of smooth access to EU markets for goods made according to new domestic rules,” she will say.
“But if that is right for jobs, living standards and prosperity then that's a choice to be made.”
Ms Fairbairn will insist that business is best served by remaining in a comprehensive customs union with the EU, which would also go a long way to addressing concerns around the Irish border.
Mrs May has rejected full membership of the customs union because it would prevent the UK striking its own post-Brexit trade deals.
But in a major speech in Warwick, Ms Fairbairn will say that the value of remaining in a customs union far outweighs the potential benefits of bilateral UK trade deals.
She will say: “There may come a day when the opportunity to fully set independent trade policies outweighs the value of a customs union with the EU.
“A day when investing time in fast-growing economies elsewhere eclipses the value of frictionless trade in Europe. But that day hasn't yet arrived.”
Remaining a member of a customs union “for as long as it serves us to do so is consistent with the result of the referendum and would be good for EU firms too”, she will say.
In a speech which will illustrate the business community's ongoing frustration with both sides in the Brexit negotiations, Ms Fairbairn will set a 70-day deadline for a written agreement on a transitional deal.
She will call for Mrs May to put forward a united UK view on the future relationship by April, with heads of terms on a final deal signed with the EU by October.
“Decisions must be taken fast, or firms will have no choice but to trigger their plan Bs,” she will warn.
“More jobs and investment will leave our shores and future generations will pay the price.”
A Department for Exiting the European Union spokesman said: “The EU has said they will offer their most ambitious free trade approach and we are confident of negotiating a deep and special economic partnership that includes a good deal for financial services - that will be in the EU's best interests, as well as ours.
“We have already made good progress, having reached an agreement with the EU on a range of issues such as citizens' rights and the financial settlement.
“But, as the Prime Minister has already made clear, we will be leaving the single market and the customs union after EU exit day.”
It comes as Tory MPs prepare to demand that Mrs May ends free movement and takes Britain out of the single market the moment the UK formally quits on March 29 next year.
Jacob Rees-Mogg, the newly elected chairman of the influential European Research Group that is made up of around 100 MPs, said it would be “absurd” to continue with the arrangements after Brexit.
He told the Sunday Express: “We must have control of free movement of people as soon as we leave” said Mr Rees-Mogg.
“This idea that we can let them carry on coming for another two years is absolutely absurd.”
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