The Bank of England said the change to the Financial Services Compensation Scheme (FSCS) would happen by 30 January 2017.
The compensation limit was lowered to £75,000 in July 2015, following sterling's rise against the euro.
But since the Brexit vote, sterling has fallen more than 10% against the euro.
The amount of compensation payable is set at €100,000 across the European Union, and under normal circumstances is re-calculated in sterling every five years.
But the European directive involved allows a more frequent assessment where there are "unforeseen events, such as currency fluctuations".
The Bank of England's move suggests that it believes the fall in the value of sterling is at least semi-permanent.
The FSCS covers current and savings accounts, and cash ISAs.
The new maximum compensation - of £85,000 per person per bank - was previously in place for five years, up to July 2015.
However Andrew Tyrie, the chairman of the Treasury Select Committee, said the level had been altered seven times in the last ten years.
"The absurd situation, in which the UK is left vulnerable, at the discretion of the European Commission, to frequent changes in our deposit scheme, must be brought to an end," he said.
"Brexit should give the UK the opportunity to set its own level of protection. We should take it."
The Prudential Regulation Authority (PRA), part of the Bank of England, will now consult on the plan, although the idea has already been approved by the Treasury and the European Commission.
The consultation will close in less than a month, on 16 December.
Banks and building societies will have until next summer to change the conditions on their publicity material.
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