Individual electoral registration (IER) should be abandoned for some groups to avoid a disastrous plunge in turnout, the Labour party has said.
The opposition called for the switch to individual registration to be scrapped for students and people in care homes - who are most at risk of falling off the register.
It follows the news that "data matching" has successfully verified the details of 87% of current electors who have been transferred automatically to the new IER registers.
However, the details of 5.5m existing electors - or 13% of the total - have not been matched or transferred, the Electoral Commission revealed.
Stephen Twigg, Labour's constitutional affairs spokesman, pointed to evidence that just 10% of students in halls of residence in Manchester were registering under IER. He said: "We have concerns about the speed with which the government are implementing individual voter registration.
"The principle is sound; it is the speed of implementation that concerns us. In relation to certain groups, there is real concern about a large number of people falling off the register. There is a case for saying that the legislation should be changed to allow students who live in halls of residence to be automatically registered, in view of those unique circumstances.
"The other group that I am concerned about is those who live in residential homes -- often older people or people with learning difficulties or other disabilities -- who may fall off the register."
But, in reply, Sam Gyimah, a Cabinet Office minister, said the debate was dogged by "bombast, hyperbole and conspiracy theory".
He said more than 410,000 16 to 24-year-olds had already applied to register via the new online system, while universities were helping town halls chase up missing students.
Gyimah said: "We cannot ignore the importance of accuracy. Without an accurate register, we risk undermining the very elections on which the system is based."
IER - which replaces the household registration system - is described as the biggest change to the electoral registration system in almost 100 years.
But no fewer than 25 local authorities have matched under 80% of voters, with Hackney (61%) bringing up the rear.
It is followed by; Brent (69%), Reading (70%), Cambridge (71%), Kensington and Chelsea (71%), Oxford (71%), Haringey (72%), Redbridge (74%), City of London (75%), Manchester (75%), Windsor and Maidenhead (75%), Ceredigion (77%), Islington (77%), Lambeth (77%), Lewisham (77%), Tower Hamlets (77%), Waltham Forest (77%), York (77%), Barking and Dagenham (78%), Adur (79%), Camden (79%), Newham (79%), Southampton (79%), Southwark (79%) and Worthing (79%).
Anyone who was not able to be transferred has been sent a letter asking them to provide additional information - their National Insurance number and date of birth.
Next summer, the Electoral Commission will recommend the IER rolls should be adopted from December 2015 - or be held back for a further 12 months, if voters risk being disenfranchised.