An estimated 800,000 people have dropped off the electoral register since the new system of individual sign-ups was introduced, according to Labour.
The party said it feared students in particular were a "casualty" of the move away from household registration after an analysis suggested some university cities had seen electoral roll reductions of up to 13%.
The Government previously defended the decision to finalise the individual electoral registration (IER) change in time for polls in May this year, saying it would remove "phantom voters" and reduce electoral fraud.
But Labour's shadow minister for young people and voter registration Gloria De Piero said: "About 800,000 people are missing from the electoral register. The Government ignored independent warnings not to rush through IER, and now it appears that students are a casualty of their hasty changes.
"The Government can act by issuing guidance to universities to support them with voter registration - we hope they listen."
Ms De Piero has written to constitutional reform minister John Penrose calling for universities to be issued guidance to offer voter registration to students when they enrol.
She said areas including York, Cambridge and Dundee West were among the worst affected by the switch to IER and also cited Sheffield University's opt-in initiative as a model for other institutions.
Some 67% of Sheffield students were registered, the MP said, and uptake at universities in Cardiff and Leicester also had a "big impact".
In the letter, she said: "As you will know, IER prevents universities from block registering all their students in halls of residence, but measures should be taken to ensure that it is as easy as possible for individual students to register.
"I write to you today to call for official guidance to be issued to every vice chancellor in the country about how they can adopt the Sheffield model in their universities for next year's enrolment.
"This would be an important step forward in rectifying the big drop in student registration and representation resulting from the Government's rushed changes to voter registration."
Before the move to IER was completed earlier than planned last year, the Electoral Commission warned that the truncated transition process could leave some of the 1.9 million people still listed under the previous regime without a voice.
But Mr Penrose said allowing "carry forward" electors to remain eligible for longer "will pose an unacceptable risk to the accuracy of the register".