Chancellor George Osborne's message to banks comes after the Parliamentary Commission on Banking Standards, which was set up in the wake of the Libor rate rigging scandal, called for a reserve power for full separation if banks did not implement reforms.
Mr Osborne had warned the Commission, against "unpicking the consensus" over reform proposals in the Bill in November, but appears to have heeded their warnings that loopholes could easily develop.
Sir John Vickers, who chaired the Independent Commission on Banking (ICB), has also said he "would not resist" a complete break up of banks if so-called ring-fencing fails to achieve its desired effect.
But the announcement will put the Chancellor on a collision course with the banks, which claim the legislation will damage London's attractiveness as a global financial centre.
More top news
Elsewhere, a cloudy and very mild night.
After a health scare, Nazanin Zaghari-Ratcliffe has been told by a specialist that lumps on her breasts are most likely not cancerous.
The US President said more sanctions would be imposed under a campaign of "maximum pressure" on the North Korean regime.