Business secretary to announce plan that has chancellor's approval and will help companies struggling to secure high-street funds

George Osborne has agreed to set aside £1bn to establish a British business bank to help small- and medium-sized enterprises, Vince Cable will announce on Monday.

In what Liberal Democrats are hailing as one of the major announcements of their conference, the business secretary will say that the new bank could leverage up to £10bn to help businesses struggling to find funds from high-street banks.

Cable, seen as the leading candidate to succeed Nick Clegg in the event of a Lib Dem leadership contest, will highlight his credentials on the left by saying he is working to develop a state-backed institution.

The business secretary will tell the conference in Brighton: "We need a new British business bank with a clean balance sheet and an ability to expand lending rapidly to the manufacturers, exporters and high-growth companies that power our economy. Today I can announce we will have one. I am working with the chancellor to develop a state-backed institution that will combine up to a billion pounds of new government capital with a larger private contribution."

Clegg signalled in a Guardian interview last month that a business bank would be created when he said the government needed to bypass Britain's "broken banking system". The deputy prime minister said: "The effects of 2008, the heart attack in the banking system, [have lasted] much longer than we feared."

The Lib Dems say they have had to fight hard to persuade the chancellor to sign up to the bank, which will be funded from "underspends" by Whitehall departments. These are the funds that remain unspent by departments, which are then clawed back by the Treasury.

Osborne is likely to be relaxed at the Lib Dem claims that they have to work hard to persuade him of the need for such a bank. It was first signalled by Downing Street earlier this month when the coalition announced a series of growth measures.

Cable hopes the £1bn of state funds will be matched by slightly more than £1bn from the private sector. He hopes this will then leverage a total of £10bn into a wholesale bank modelled on the KfW banks in Germany and the Small Business Administration in the US.

The bank will not have branches in the high street and will act as a wholesale institution. It will aim to make loans to small- and medium-sized enterprises through innovations such as peer-to-peer lending, run by companies such as Zopa, in which individuals bypass traditional banks to lend to each other.

The business secretary said last night: "The government understands the frustration felt by many small- and medium-sized businesses around securing credit, especially from the big four retail banks. Many new, promising, growing companies simply can't get the loans they need to expand on reasonable terms. Manufacturers, exporters, startup companies are struggling to finance growth. We are going to help fix this."

Chuka Umunna, the shadow business secretary, said: "Labour has led calls for a British investment bank since last year. It is crucial that this business bank is more than merely a rebadging of existing schemes [and] that it gets credit to profitable firms that can't access it."

The speech by Cable will be the most significant moment of the Lib Dem conference after Clegg's speech on Wednesday. The business secretary confirmed in the Sunday Times that he would stand for the leadership if a vacancy arose.

Senior Lib Dems believe there is no threat to Clegg, who tried to stabilise his position by apologising for his decision to break a written pledge not to raise tuition fees. But the deputy prime minister is expected to face a difficult conference next year if his ratings have not improved by then.