The software is overloaded with detail, say councils, because the government wants codes for every course at every college to be fed into it.
Edward Lister, Tory leader of Wandsworth LBC, where 2,000 students are applying for loans, said the DfEE was at fault.
'More than 150 councils up and down the country have been forced to change their systems to suit the new centralised arrangements. The task has been further complicated by the excessive red tape the DfEE has insisted on,' he said.
Liverpool City Council, where another 2,000 students could be affected, said: 'We do still have outstanding technical problems and are in serious negotiations with software people.
'We can't say at the moment if there will be delays but we are working very hard to make sure there won't be and looking at back-up arrangements.'
Manchester City Council has hired extra staff to cope with the crisis. It said: 'We have a dedicated team working extremely hard and every effort will be made to clear the backlog by September.'
Others were less concerned. Brighton and Hove Council said: 'Work to ensure a smooth transition for students has gone well. Student support staff are up to date and expect to start sending out financial notifications to new students this week.'
The DfEE would not comment on whether contingency plans were being made.
It said: 'It's our firm expectation that students will get paid on time. We have no reason to believe any authority will be unable to deal with student applications.'
Councils used to assess and pay out on loan applications. Now they only make the assessment while payments are made by the central Student Loan Company.