The survey found the biggest increases in demand for postal voting were in Birmingham and Woking.
So far, 90 people had complained they had not received their postal voting packs, Mr Riordan said.
And in some wards, scattered across the country, postal voting is being promoted.
He wondered if Mr Prescott felt there had been an error of judgement over the issue of postal voting.
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About 2, 100 postal voting packs may have gone missing in Leeds ahead of the local elections, it has been revealed.
The Electoral Commission said that the process needs to be tightened even though it believes postal voting should remain in place.
The commission will produce its report on the trials of all-postal voting at this year's local elections at the end of July.
The Conservative Party also claimed last week that postal voting was in danger of bringing about a return to "18th Century fraud".
Probably the most significant question was Mr Ancram's on the alleged chaos and even fraud in the experiment on postal voting for the elections.
The act also eased the restrictions on postal voting, a provision that has placed a large question mark over the probity of British electoral arrangements.
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Some polling stations were open over the weekend or in supermarkets, while some councils have also used mobile polling statoins, electronic voting and more postal voting.
In the recent elections, there were all-postal voting pilots in four English regions - the East Midlands, the North East, the North West and Yorkshire and the Humber.
BBC: NEWS | UK | Politics | Council chief warns on vote fraud
These include adopting measures currently used in Northern Ireland, such as restricting postal voting to constituents that are physically unable to come in person and forcing people to prove their identity at polling stations.
"There is a huge gap between the law and the Electoral Commission's code of conduct for political parties, candidates and canvassers on the handling of postal voting applications and postal vote ballot papers, " says the letter from Sir Albert.
BBC: NEWS | UK | Politics | Council chief warns on vote fraud
"'On demand' postal voting is so difficult to control that I might go so far as suggesting that we should revert to the pre-2001 regulations if we cannot find a way of preserving the integrity of the process for the individual voter, " said Sir Albert.
BBC: NEWS | UK | Politics | Council chief warns on vote fraud
The measures follow allegations of widespread electoral fraud, including vote-rigging, in the UK since postal and proxy voting were greatly extended in 2001.
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Advance voting, curbs on campaigning activities at polling stations and restrictions on the handling of postal vote applications are also among options put forward in its consultation on reforms.
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