At present, payouts for savers with failed banks can take weeks, leaving many customers concerned about access to money in the interim.
Transferring customers from a failed bank to another should also now be easier.
One of the Bank of England's formal objectives under the act is to maintain stability.
Peter Thal-Larsen, banking editor of the Financial Times, told the BBC's Working Lunch programme the act will basically allow financial authorities to take early action to move savers' deposits from a failing bank before tackling other problems.
"The idea is that, if there is a bank that gets into trouble, to insulate it and make the wider impact of that less, but I don't think they can actually stop banks from getting into trouble in the future," he said.
Colin Melvin, chief executive of Hermes Equity Ownership Services, said: "We welcome the new Banking Act and the enhancement it will bring to the regulatory framework, including the strengthening of the Bank of England.
"However, we need to do more to stimulate growth and restore confidence and trust in the financial sector."
The new laws make permanent temporary laws introduced in the wake of the collapse of Northern Rock, which was nationalised after confidence in it disappeared.
BBC business correspondent Joe Lynam said that until recently it was unusual for Britain's banks to apply for emergency funding from the Bank of England due to the stigma attached and the ensuing drop in confidence.
Northern Rock's very public appeal for funds accelerated its demise 18 months ago.
The new legislation is unlikely to prevent banks collapsing but it arms the financial authorities with the ability to act behind the scenes in the overall interest of the economy, our correspondent adds.
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