The BoE has very limited powers to set direct regulations for clearing and settlement, processes that ensure that legal ownership is exchanged for cash and custody in a stock and bond trade.
Rules for the industry inherited from the European Union following Britain's departure from the bloc are the legal responsibility of parliament and government, meaning laws would need changing to update them, a cumbersome process.
In a paper for public consultation, the finance ministry said on Monday it proposes more extensive delegation of regulation to the BoE, though still working within policies set by the government and high international standards.
It would allow the BoE to take enforcement action, waive or modify rules, and open investigations, with maintaining financial stability the overriding aim.
There will be a secondary objective of supporting innovation in a sector where blockchain is making inroads to cut costs.
The EU has said it will extend temporary permission from June for banks in the bloc to continue using clearers in London.
Brussels, worried about not having enough say over foreign clearers during times of market crises, wants chunks of the euro business relocated from London to the bloc.
The ministry said the BoE should consider the potential impact of its decisions on jurisdictions with significant exposures to clearers in Britain.
Britain is considering making it explicit that the BoE must ensure that its regulation is based on financial stability risks and not on the basis of "nationality or location of users", the ministry said.
The ministry will separately be consulting on the regulatory perimeter for systemically important firms in the payments sector in the first half of 2022.
(Reporting by Huw Jones; Editing by Susan Fenton)
By Huw Jones