The Treasury will need to find almost £2bn a year to fill the hole left when EU funding for some of Britain’s poorest communities ends after Brexit, ministers have been told.

A body that represents local authorities in the industrial areas of England, Scotland and Wales said the government needed to match the money currently coming from Brussels and allow for extra EU cash that would have arrived over the next few years.

The Industrial Communities Alliance said the new shared prosperity fund – designed to replace EU funding to the regions – needed to be at least as generous as the schemes it was replacing.

It urged ministers to take advantage of the freedom provided by Brexit to broaden the scope of the fund so that it could tackle a wider range of problems than allowed under EU rules.

Russell Imrie, acting national chair of the ICA, said: “Many voters in older industrial Britain backed Boris Johnson. Now is the time for him to ensure that our communities do not lose out from Brexit and to support our efforts to rebuild the economies of our areas.

“Thanks to European funding over the years, we’ve been able to make progress in replacing the thousands upon thousands of jobs lost from industries such as coal, steel, engineering and textiles, but we still have a long way to go to match the prosperity in other parts of the country.

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“We want to see the prime minister’s electoral promise translated into hard cash and real action on the ground to help deliver the jobs and growth that our communities still so clearly need.”

The UK currently receives £1.4bn a year from the European regional development fund and the European social fund and a number of smaller payments. However, the ICA said that after adjusting for inflation and the fact that more UK communities would be eligible for EU funding were it not for Brexit, the budget for the shared prosperity fund needed to be £1.8bn a year.

It added that the range of activities on which EU funds could be spent had become too restrictive and the creation of the UK Shared Prosperity Fund allowed a fresh start. “There is a strong case for greater flexibility in spending in order to tackle a wider range of regeneration issues than those presently addressed by EU funding.”