Around six million UK citizens of all ages have yet to fill out the forms that will allow them to take part in the June 23 vote - and more than one million of those are under-25.
Liberal Democrat former leader Lord Ashdown said: "The risks of not registering, and not voting are now very clear.
"The Leave campaign's vision of Britain is one that is divided and weakened. We cannot let them succeed.
"If we do not now pull out every stop to get people registered and get them to vote, then we risk a lost generation for Britain's young people outside the EU."
The push to encourage voter registration came as six former Labour leaders issued a plea for the party's supporters to vote Remain, warning: "If Labour stays at home, Britain leaves."
In an open letter released by Britain Stronger in Europe, Lord Kinnock, Dame Margaret Beckett, Tony Blair, Gordon Brown, Harriet Harman and Ed Miliband warned that Labour voters could not afford to opt out of involvement in what many see as an internal spat between Conservatives. "Only Labour can save Britain from Brexit," they said.
Labour's traditional working-class supporters have "the most to lose if we leave, but also the most to gain if we remain", said the letter.
Observers believe Labour voters could hold the key to the outcome of the referendum, with Remain strategists concerned that a low turn-out by the party's supporters could hand victory to the Leave camp.
While polls show the party's voters are significantly more likely than Conservatives to back Remain, they are also less likely to take part in the referendum - with a recent survey finding 52% of Labour voters saying they were "certain to vote", against 69% of Tories and 71% of Ukip supporters.
Brown, speaking at the Hay-on-Wye Festival, called for a "positive, principled and progressive" message to persuade people to back Remain to support jobs, security and fairness.
In the letter, the six wrote: "Europe protects people at work; stimulates jobs and innovation; keeps prices lower; leads global action against climate change; makes us safer against terrorism; and magnifies Britain's voice and values in the world.
"But make no mistake: this would be lost if we leave. Labour communities would face a double threat: the return of recession, led by a Tory government with an emboldened right wing.”
Meanwhile, First Minister Nicola Sturgeon has confirmed she will take part in an ITV debate on the EU referendum this week.
The broadcaster has yet to disclose Thursday's panel, but former London Mayor Boris Johnson is widely expected to appear on the platform for the Leave side.
The televised debate will follow a head to head between Prime Minister David Cameron and Ukip's Nigel Farage, to be shown on the channel on Tuesday.
Sturgeon said: ''I have been invited to take part as SNP leader and First Minister of Scotland, and I want to make the positive, progressive case from a Scottish perspective for remaining in Europe.
''But the message about why we believe staying in the EU is better for jobs, workers' rights, prosperity and security will be one for an audience across the whole of the UK."
ITV said "senior political figures" from both the Leave and Remain sides will take part, which will be in front of a live studio audience in London.
Energy Secretary Amber Rudd and shadow business secretary Angela Eagle are among those who have been tipped to join Sturgeon in arguing the case to remain in the EU.
The Remain camp has been hopeful of victory in the referendum, but senior pro-EU figures are becoming gloomier as the June 23 vote draws closer.
Several Remain sources told the Sunday Herald that hostility to immigration is helping the Brexit campaign.
A win for Leave is likely to trigger the immediate resignation of Cameron as Prime Minister, as he has put his credibility on the line by backing Remain.
Cameron attacked Tory colleagues Michael Gove and Boris Johnson for "writing cheques they know will bounce" after they claimed Brexit would free up an extra £100m a week for the NHS.
Diverting the UK's contribution to EU coffers would give the straining health service a "cash transfusion", the duo have claimed.
However, the Prime Minister countered by saying the economic impact of Brexit would mean less money for the NHS.
Johnson also claimed yesterday that around 300,000 new jobs will be created if Britain is liberated from the "shackles" of the European Union.
Leave campaigners have pledged to launch immediate trade negotiations that would create an employment boost if voters back Brexit in the referendum.
Cameron said: "The Leave campaign is writing cheques they know will bounce, 9/10 economists say there'll be a profound shock if we leave the EU. That means there will be less money - not more. It's also why so many doctors and nurses support remaining in the EU."