The DWP explained, in a statement, that the timeline is due to the fact that it "will be working in partnership with employers and the pensions industry, learning from the contribution increases in April 2018 and April 2019."
A spokesman for the DWP said: "This will ensure that businesses and savers have time to plan for the changes and that we continue to build on the foundation already in place in an effective way."
Rachel Vahey, product technical manager at Nucleus, said this review was an important step "in clearly showing contributions need to be raised above their current level to give people the money in retirement they both expect and need."
She said: "The DWP now needs to move forward and put in place plans to start increasing contributions."
Darren Philp, policy director at workplace provider The People's Pension, praised the review, saying that the "government has listened to growing calls from the pensions industry to strengthen auto-enrolment".
According to Mr Philp, "it is bizarre that since the inception of auto-enrolment, people's contributions have not been based on their entire salary."
He said: "The People's Pension has long-called for this to change as we believe it is nonsensical and adds an unnecessary layer of complexity to an already complex system.
"We are pleased to see that people will now be supported to save more as contributions will now start from the first pound of someone's pay packet."
According to Nathan Long, senior pension analyst at Hargreaves Lansdown, the measures announced "will transform people's retirement prospects".
He said: "Not only does this mean retiring with more income, it means having greater control over leaving work. These measures mean someone with average earnings could increase their pension pot at retirement by over £60,000."
However, Mr Long said he is disappointed with the recommendations made by the DWP to include the self-employed in saving for retirement.
He said: "Policy makers must be prepared to use the tax return system to automatically enrol this group to truly solve their pension problem."