In its mandate for trade talks with Brussels, Britain said a deal should provide a "predictable, transparent and business-friendly environment" for cross-border financial services activities.
"The agreement should include legally binding obligations on market access and fair competition," the document said.
The EU has spoken only of "voluntary" cooperation in financial regulation.
While a formal EU-UK trade deal would be legally binding once ratified, the European Commission said on Thursday that financial market access would not be included as that was a unilateral decision by Brussels.
The financial sector has said that the EU system of market access, known as equivalence, is opaque and far patchier than Britain's current unfettered access. It can also be withdrawn in 30 days, making it unreliable.
Britain says it wants arrangements that will allow regulators on both sides to cooperate and build "enduring confidence" that can deal with rules as they "evolve".
Britain fears that the EU would seize on any divergence from EU financial rules as an excuse for what incoming Bank of England governor Andrew Bailey called a "punch-up" with UK regulators, leading to a denial of access.
Markus Ferber, a senior German centre-right member of the European Parliament, which can veto an EU-UK trade deal, said EU and UK rules would evolve over time.
"There needs to be a mechanism to ensure that equivalence is maintained five years down the road. Regular reviews of the equivalence status are therefore necessary," he said.
Britain and the EU had already agreed to assess each other for financial market access by the end of June and both sides restated this on Thursday.
The mandate says that Britain has left the bloc with the same rules as those obtaining in the EU, thereby providing a "strong basis" for concluding assessments on time.
Britain says these should be "distinct" from talks on a free trade agreement.
But a senior aide to Michel Barnier, the EU's chief trade negotiator, said last week that completing assessments in June would not mean an actual decision on access.
This would factor in progress on a wider UK-EU free trade agreement in obtaining access to UK sectors such as fisheries, the aide said.
Barnier said on Wednesday that UK financial firms that want certainty in their relations with EU customers can set up subsidiaries in the bloc, which over 300 have done.
For the others, there was the equivalence route.
"But these equivalences will never be global nor permanent. Nor will they be subject to joint management with the UK. They are, and will remain, unilateral decisions," he said.
Bankers say the EU is likely to grant only temporary access while euro activities are relocated from London to the bloc.