The UK has 3.5bn euros (£3.1bn) of capital at the bank and a House of Lords report said the UK’s investment could be worth 10.1bn (£8.9bn) euros taking into account reserves and profits.
Established in 1958, the EIB uses capital provided by EU countries to make loans at low rates, often for major infrastructure projects.
All 28 EU nations are shareholders in the Luxembourg-based bank, with the UK being the largest alongside Germany, France and Italy.
Mr Stubb, a former prime minister of Finland, told the BBC that the UK’s money could be tied up for decades in after it leaves the EU in 2019.
“Everyone on both sides of the negotiating table agree that we have to pay back the 3.5 billion euro, basically in cash, and that will happen over a long period, up until 2054, because that’s when the loans are amortised.”
He insisted that no-one in the bank wanted to “punish” the UK for leaving and actually wanted to “alleviate the pain” of Brexit.
“I have a British heart pumping, I am married to a Brit, my children have dual nationality and I think Brexit is one of the biggest travesties that we have seen in the modern era,” he said.
“So I will do everything in my power to alleviate the pain, but the economic facts are just such that there are no winners in Brexit – apart from perhaps a few lawyers. Unfortunately, we will see this in the coming years.”
The BBC’s Ross Hawkins said Today had heard how delays in authorising new loans while the UK remains part of the EU could see fewer social homes built.
One housing association, Stonewater, said it may build around 300 fewer homes because its application for £100m to build new properties had ground to a halt.
Its executive director John Bruton told the programme: “The Bank has been waiting for assurances from the UK government before the application can be progressed.”