A report compiled by Mr Straw, The Missing Millions: Britain's Disenfranchised Citizens, claimed one in five people in their early 20s had not signed up to vote.
It estimated that nearly a quarter of black people and 38 per cent of those relying on a private landlord to fill in registration forms did not appear on the register.
Mr Straw said his report was 'an indictment of Home Office indifference'. The proportion of people registering had declined each year since the Tories took office in 1979, he said.
He rejected calls for a legal obligation to vote, but called on the Government to campaign to increase registration among young people and for minimum standards for local authority voter-registration drives.
'The right to vote is the most basic right in a democracy. It is deeply alarming that in Britain today two million people are denied that right,' he said.
'So great is the crisis that only one in three young black men living in private rented accommodation are registered to vote.'
The report claimed Tory- controlled Westminster had the lowest level of voter registration in the country, at 67 per cent. That figure was contested by Westminster Council, which claimed 80 per cent, while pointing out the borough had a high transient population.
Mr Straw said ministers knew that many of those not on the electoral roll would vote Labour and were not concerned to tackle the problem.
Councils compile registers each autumn and registration forms are currently being sent out. Voters registering by 10 October will be included in the Electoral roll, published in February.Reuse content