Labour says its proposals on the EIB underline the need for Britain to remain in the EU.
Labour's proposal aims to bring the UK's per capita share of funding, which currently stands at 20,000 homes per year, into line with the EU average.
In its proposals, Labour says that if the UK moved to the EU average of per capita EIB investment then it would increase funding from €7.1bn last year to €10.1bn.
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This, says Labour, could mean a possible annual €3bn increase in funding (almost €12.7bn by 2020) available for UK businesses which, it says, could be used to help tackle issues like the UK's housing crisis.
For example, if applied next year Labour argues that it could fund 40,000 homes a year, which over the next four years to 2020 could mean 160,000 new affordable homes.
There is also the potential of an additional 65,000 jobs each year, it says.
Speaking on Monday, John McDonnell, Labour's shadow Chancellor, said: "Labour wants to remain and reform Europe so that we can better use the levers of power inside the EU to ensure our country punches its weight in the world and better delivers for all working people.
"The opportunities to build a better world will be with a Labour vote to remain in the EU, not a Tory Brexit. Labour wants to build a better Europe and that can start by using the EU to increase investment that could be used to build more homes here, and help tackle the Tory housing crisis."
Elsewhere, Labour's Hilary Benn and Angela Eagle will on Monday challenge the Leave campaign to "come clean" on which of the UK's "hard-won workers' rights" they want to scrap if Britain votes to leave the EU.
Labour asserts there are concerns about what would happen to the rules protecting workers in the event of a vote to leave the EU.
Priti Patel, a Leave campaigner and Tory employment minister, has claimed that, "if we could just halve the burdens of the EU social and employment legislation we could deliver a £4.3bn boost to our economy and 60,000 new jobs."
Her colleague Boris Johnson said EU employment regulations were "holding back" growth and described Britain dropping its insistence on changes to EU employment law as "very disappointing".
Labour's recommendation comes as latest polling shows the Brexiteers now stand on 43 per cent, while 40 per cent say they support the campaign to keep the UK in the EU.
The poll, published in a newspaper on Sunday, suggests the Remain camp has lost four percentage points in the last two weeks, during which Boris Johnson and Michael Gove have relentlessly campaigned on the theme of immigration.
Former British Prime Minister John Major hit out at "inaccurate information known to be inaccurate" being spread by the "squalid" and "deceitful campaign" of the Brexiteers.
He said on Sunday that Johnson, Gove and others deliberately overstate by three times the net contribution British taxpayers make to the EU budget.
Elsewhere, diplomatic sources say China has given coded support for the Remain camp by calling for a strong, united Europe.
Yao Ling, deputy director of a research centre under the commerce ministry, said in a ministry-run newspaper, "Of course, if you are investing in Britain as a way into the European market, using Britain as a bridge into the EU's 27 other nations, then once Britain leaves the EU, that bridgehead will be curtailed."