Theresa May’s reported plans to demand the return of £9bn of UK assets held by the European Investment Bank would put in jeopardy funding for key British infrastructure projects, including the government’s flagship Midlands Engine.

Over the weekend, it was claimed that the prime minister intends to reduce the size of Britain’s divorce bill from the EU by threatening to pull out the UK’s share of assets in the bank.

A Whitehall source told the Sunday Times that the EU would be worried because the European Investment Bank’s (EIB) investments in infrastructure across the EU are “predicated on our contribution”.

However, a senior source close to the bank based in Brussels has told the Guardian that the threat would only put in peril projects in the UK with applications for loans currently under appraisal by the member states, who comprise the EIB’s stakeholders.

Such projects include a £122m loan to the “Midlands engine”, which the prime minister claimed in January would be “an engine for growth” to rival George Osborne’s “northern powerhouse”.

The source said: “There will be greater scrutiny by other member states. You can expect the tone of negotiations to influence the approval process going ahead. You can’t rule out grumpiness all round.

“As things become political, to be honest, I think we will expect more comment from the EU-27, backbencher types, saying if the UK is leaving how on earth can they reap the benefits.”

Tim Farron, the leader of the Liberal Democrats, in response to the development, accused the prime minister of being reckless in her approach to the coming article 50 negotiations.

He said: “The Midlands engine is facing a false start. This is another sign of the chaos and incompetence at the heart of this government.”

Britain has been a member of the bank since 1973. The bank has made loans of more than £52bn in the past decade to UK-based projects, including £5.5bn last year supporting schemes such as schools, universities and new hospitals.

Crossrail also secured €600m (£523m) in 2013 to help buy rolling stock for the high-speed Transport for London service due to open next year. London Overground secured £220m last April to help buy 60 trains.

Funding agreements that have already been signed off by the EIB’s members will not be affected by the uncertainty caused by the article 50 negotiations, as they are legally binding.

However, those under appraisal could be jeopardised by aggressive briefings from Whitehall about the future, it is claimed.

The chancellor, Philip Hammond, launched the government’s strategy for the Midlands last week, during a visit in Dudley. An application for EIB funds was made in January.

However, the EIB believes that there is a particular danger for recipients who require certainty of its funding streams well in advance of spending the money, such as water companies.

A source claimed that utility companies used EIB funding to keep prices to consumers down. “In the past they have always known that for half of the investment needs, they know what the pricing will be,” the source said. “It is very easy. Clearly, now there is an uncertainty looking ahead.”

Under the statutes of the EIB, its shareholders can only be member states of the EU. However, it had been hoped by many in senior positions in the bank that “rational thinking” would lead to an amendment to the rule book to allow the UK to stay.

According to the EIB’s 2015 financial statements, the bank’s reserves consist of paid-up capital from member states of €21.7bn, plus a further €41.6bn of accumulated profits. The UK’s share of this is 16.1%, or €10.20bn (£9bn). However, there is some doubt in the EIB that Britain would be eligible for that full share if it left, given that the bank is not winding down, the source added.