Business leaders have urged the government to expand its Covid-19 rescue schemes to prevent thousands of businesses from going bust, as figures showed lenders have approved fewer than half of the applications for state-backed loans made to date.

The CBI said ministers needed to address shortcomings in the loans scheme for small and medium-sized businesses, under which 16,624 firms have borrowed £2.8bn to date, up from £1.1bn a week earlier.

Carolyn Fairbairn, the director general of the CBI, said that without an extension of the coronavirus business interruption loan scheme (CBILS) and a fresh round of grants for small companies that failed to qualify for loans, the Covid-19 crisis would push thousands of previously solvent firms to the wall.

Fairbairn said a scheme for the smallest companies that need to borrow less than £25,000 should be created and supported with 100% government-backed loans. A scheme offering loans of up to £500,000, with 80% covered by the state, should be upgraded to have 100% of the loan covered by government guarantees, she said.

The latest weekly data released by the banking lobby group UK Finance on Thursday showed that lending under CBILS had reached 16,624 firms. That is just 40% of the 36,000 formal applications lodged with banks so far.

While approvals have increased from a 21% rate a week earlier, critics are still concerned that banks are not able to get money fast enough to businesses that need it most.

UK Finance has not yet confirmed how many applications have been rejected, and it said the remaining figure accounted for both rejections and loans still being processed.

In France, commercial banks have processed loans under a similar scheme and distributed about £20bn to more than 170,000 firms.

The British Chambers of Commerce and the Federation of Small Businesses have also campaigned for reforms to the current arrangements.

The BCC’s head of economics, Suren Thiru, said: “The increase in companies accessing CBILS is encouraging progress. However, the number of applications processed and approved will need to be increased significantly in what is a crunch week for firms urgently trying to access financial support. A concerningly high number of businesses are still finding accessing the scheme too complex and too lengthy.”

Ann Francke, the chief executive of the Chartered Management Institute (CMI), said a survey of its members found that a third of small and medium-sized company managers felt existing measures would not ease their financial distress.

“We urgently need to streamline the execution by which funds and support get to businesses with simple, fast processes, clear accountability and communication. This needs better management,” she said.

Stephen Jones, the chief executive of UK Finance, said the banking industry understood the critical role it was playing during the outbreak and frontline staff were working tirelessly to get money out to viable businesses as quickly as possible.

Some lenders have been more successful in getting cash out to struggling businesses than others. Royal Bank of Scotland alone accounts for about 40% of the total number and value of loans issued to date, having approved 6,518 loans worth £1.1bn. That is down slightly from its 50% standing a week earlier, suggesting some of its peers are starting to gain ground.

Barclays has approved 2,971 loans worth £586m to date, while HSBC has issued 3,539 loans worth £480.5m. Lloyds said it had issued £335m after approving around 80% of the 2,876 formal applications it received so far.

The business secretary, Alok Sharma, was questioned by MPs on the business, energy and industrial strategy committee on Thursday and acknowledged that loans to small firms needed to be processed more quickly.