According to the Times, up to 100 councils are having problems with the new software and some have begun to draft in extra staff to help with a manual vote should this become necessary.
David Monks, chief returning office for England, told the paper: "It is essential that we have the systems working by next week so that we can start processing postal vote applications. If not, returning officers will have severe difficulties and the results could be delayed."
The government has introduced a number of measures to improve the postal ballot system, including an Electoral Commission agreement with the three main parties to a new code of conduct which aims for the "strengthening of the integrity" of the postal voting system.
Postal voters were for the first time required to supply their signature and date of birth when applying to vote and this data will them be matched electronically with ballot papers.
But in some local authorities, despite the software having arrived, staff have not been trained in how to use it, the Times report claims.
A spokesperson for Department for Constitutional Affairs said that any difficulties with software systems would not prevent postal voters from casting their vote and having it counted.
"It is important to remember that the majority of postal votes are received before polling day, and will be checked and verified at opening sessions before polling day, so that on polling day itself the postal votes are ready to be counted," she said.
"Systems are being supplied by a number of commercial companies which have developed new software and hardware for the new postal voting provisions. They have all given assurances that they will have the appropriate systems in place for the May local elections."
Malcolm Dumpster, policy director for the Association of Electoral Administrators and deputy returning office at Southampton City Council, told the Today programme that the system should have been piloted.
"I think there is a fear that if systems go down, if people have real problems in saying, yes, that's a good signature, a bad signature, open to challenge, confidence goes in the election and that's just what we don't want in this climate," he said.
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