The PRA has already forced big lenders to meet or exceed the new rules and Friday's consultation largely covers how smaller banks and other financial institutions must also comply.
It estimates that big deposit-taking banks face an annual cost of £9.5bn at most to comply with the rules.
But investment firms - which exclude deposit-taking banks - will have to find £35bn to £43bn to comply with the new rules, the PRA said.
This total would fall to £27bn to £29bn during the phase-in of the new rules which runs to 2018 if balance sheets were "adjusted", the PRA added.
"The lower estimate reflects the reduction in risk, and therefore risk-weighted assets, that investment firms may hold once they have adjusted to the... requirements," the watchdog said in its consultation paper.
The EU bank capital requirements law implements new global standards known as Basel III in the 28-country bloc, forcing banks to roughly triple the amount of capital they must hold compared with before the 2007/09 financial crisis.
The EU rules also force banks to build up cash buffers from 2015 to withstand market shocks.
The PRA said it would continue to use its discretionary powers to make sure firms hold enough cash until the EU rules come into effect, signalling there will be no temporary relief.
A third element of the EU rules is a new limit on balance sheets in relation to capital levels, known as a leverage ratio.
The PRA, which is forcing big banks to comply early with this rule, signalled on Friday it will give smaller firms breathing space.
The watchdog will consider at a later date whether the smaller banks and building societies must also start disclosing their leverage ratios before the EU's 2015 start date.