May's white paper had called for equivalence to be "expanded", explaining it was "not sufficient to deal with a third country whose financial markets are as deeply interconnected with the EU's as those of the United Kingdom are".
The EU has been clear since March that it wants full autonomy and control over how United Kingdom banks operate in the bloc after Brexit, rejecting proposals for joint oversight and insisting that the system USA banks are subjected to, known as equivalence, is all that's on offer.
Mr Raab appeared alongside the Prime Minister' Europe adviser Olly Robbins in front of MPs amid increasing Brexiteer concerns about the influence of the senior civil servant.
"The EU can not and the EU will not delegate the application of its customs policy, of its rules, Value-Added Tax and excise duty collections to a non-member who would not be subject to the EU's governance structures", he said.
Former Brexit secretary David Davis said in an interview that there would have to be a "reset" when the government would have to give up Chequers and start afresh, the report added.
"I am going to bring to (Michel) Barnier and to the whole enterprise as much energy as I can".
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At the heart of the conundrum lies an European Union insistence that the way to avoid a "hard border" is for Northern Ireland to follow European Union rules as in Ireland and, if need be, different from those on the British mainland, while May rejects new barriers to goods moving from the mainland to the troubled province.
Unveiling the plans in a white paper in the House of Commons, Mr Raab described it as "another key milestone in the UK's path to leaving the EU".
Barnier said any customs arrangement or union "must respect this principle".
He highlighted agreement on security measures and said both sides wanted a wide-ranging free trade deal. But he had added: "On our future economic relationship it comes as no surprise that finding common ground between the EU27 and the United Kingdom is more hard".
"We've made really good progress this week", Mr Raab said.
"In that event we see some scope for a recovery in business investment, although clearly there are material risks around this expectation", he said, predicting a slow pace of monetary tightening. Under current rules the European Union has sole authority to cut access off at 30 days' notice - a setup banks say is unwieldy, not good for financial stability, and can be open to political meddling.
On the two-year anniversary of the Brexit vote last month, more than 100,000 joined a previous People's Vote march in London calling for a referendum on the UK's final departure deal, according to organisers.