The scheme - in which adults receive up to pound;150 to help pay for learning - is set to go nationwide next year.
It is being piloted by 13 training and enterprise councils, and Labour wants the cash for learning accounts to come out of TEC budgets. But for some TECs the cost will swallow up cash reserves, bringing cuts in locally-based projects tackling social exclusion.
Education-business partnerships, training initiatives, and inward investment programmes could also be hit. TECs started individual learning accounts and some have already invested heavily in them.
Gloucestershire TEC, now part of the Link Group, has already sunk pound;1 million into ILAs and struck deals with FE colleges to offer discounts to students.
But local business leaders are unhappy about the implications of TECs funding learning accounts. Some have threatened to quit the Link Group board if its existing programmes are cut back.
Graham Hoyle, Link chief executive, said: "If we have to find all the money the Government has currently allocated to us to pay for individual learning accounts, that would take away about 90 per cent of our discretionary spend.
"The board has made it quite clear that if we get to that situation, if there's no discretionary spend there's no need for discussion - there's no need for a board."
"We are totally committed to the concept of individual learning accounts. We think they are a great idea and have got to work. But what we haven't got is a million and a half without just ripping up everything else we do."
Richard Barnfield, chief executive of neighbouring WESTEC, said the cost of learning accounts would slash its projected discretionary budget of pound;1.9m for next year to pound;750,000 in 2001 and to pound;425,000 in 2002.
"We want to do individual learning accounts, but not at the expense of everything else," he said.
A spokesman for the TEC national council said: "The council is working closely with the Government to find the most effective and least bureaucratic means of establishing ILAs.
"It remains confident that a practical solution can be found which will maintain the capacity of TECs and chambers of commerce to operate as key strategic bodies in local and regional economic development."
Richard Payne, chairman of Stroud and Swindon Building Society, has written to the TEC National Council threatening to resign as chairman of the Link Group if ILAs erode Gloucestershire's discretionary budget.
A Department for Education and Employment spokesman said: "We are aware that the capacity of TECs to fund accounts varies and we will look closely at the funding of individual learning accounts in areas which appear to face particular difficulty."
But he added that Gloucestershire and WESTEC were "in a very good position to fund individual learning accounts" and: "Our understanding is that both TECs are supportive of individual learning accounts and are planning to make them work in their areas."