While equivalence would allow firms to continue operating in the United Kingdom without submitting to direct European Union supervision, Britain has argued that the system is too one-sided.
European Commission vice-president Valdis Dombrovskis said that future access will depend on a system of "equivalence" under which Brussels will exercise "unilateral and discretionary" powers to judge whether United Kingdom regulations meet its standards. "We are already seeing progress", the City minister John Glen told the CityWeek conference in the Square Mile's Guildhall.
"But we should not let flawless be the enemy of good".
However, the Commission vice-president stressed that he believes companies from both the United Kingdom and EU27 have the capacity to "alleviate" the main risks by repapering contracts and adapting operational models.
Equivalence is already used by financial services in multiple large economies, including the US.
Mr Dombrovskis said risks and uncertainty remained not only over the EU's future relationship with the United Kingdom, but also on the Irish border and the governance of the withdrawal agreement.
He added: "Equivalence is only possible if there is close convergence of rules and supervision".
"In spite of these improvements, there are some clear limits to equivalence", he said.
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Catherine McGuinness, political leader of the City of London, the historic "Square Mile" financial district, said after Dombrovskis' speech that a mutual recognition deal would be best for Britain and the EU.
"The reality is if you want access, it's going to come at a price".
Andrew Bailey, chief executive of Britain's Financial Conduct Authority, said the equivalence regime doesn't best suit any parties, and that a mutual recognition agreement is "eminently achievable".
British regulators have said banks should be allowed to use the transition period to take more time to implement Brexit plans.
"For the moment we can not assume that such arrangements will be in place and so the United Kingdom authorities have also set out plans for unilateral action in the United Kingdom to minimise cliff-edge risks, providing continuity for firms doing business in the United Kingdom and confidence for their customers", he said in a speech prepared for the City Week conference at Guildhall in London.
The watchdog has said it will also ensure an "appropriate transition" to a new supervisory model for European Economic Area firms.
Repapering refers to moving accounts of customers from Britain to existing or new hubs in the EU27.