Previous modelling for SAGE said the number of COVID-19 vaccine doses was predicted to reach up to 3.9 million doses a week.
But in the latest paper, published on Monday, scientists expect to deliver 2.7 million doses per week in England until the end of July and 2 million after that date.
It says: "The central rollout scenario provided by the Cabinet Office is considerably slower."
Another scenario could see slightly fewer doses, at 2.5 million doses a week until the end of July then 2 million after that, the paper said.
The latest NHS England data shows 3.5 million people were given a dose in the week up to 28 March, up from 3 million the week before and 1.7 million the week before that.
The slower rollout would mainly affect those under 50 years old, the government's advisers added.
Fewer under-50s would have had the vaccine by the time step three and step four of the roadmap out of lockdown comes around, the paper says.
Step three of the roadmap is currently proposed for 17 May and will see indoor mixing allowed and pubs and restaurants to reopen inside.
Step four is the final stage of unlocking, planned for 21 June, when all restrictions are set to be lifted.
The modelling paper adds: "The lower level of population immunity means the subsequent resurgence is larger but only marginally so, given the differences in rollout speed are relatively small."
The Department for Health and Social Care warned in mid-March there would be a vaccine shortage from 29 March and second doses would be prioritised over first doses in April as a result.
Those aged 49 and younger should expect their first jab from May, going down the age groups by 10 years each time, the department said.
Part of the issue is a reduction in supply from AstraZeneca, including from its partner plant in India.
On Tuesday morning, vaccines minister Nadhim Zahawi confirmed the Moderna vaccine, which has been approved for a while, will arrive in the UK "around the third week in April" and more would come in May.
However, Downing Street sources would not say whether the new vaccine would plug the shortfall.
Two other vaccines, Novavax and Janssen (Johnson & Johnson), are yet to be approved for use in the UK, although Boris Johnson confirmed last week that Novavax is already being manufactured in the UK.
A Department of Health spokesman said: "Our vaccination programme continues to make exceptional progress - with over 37 million jabs administered so far.
"Vaccine supply was always going to vary over time, but we are on course to offer a first vaccine dose to those aged 50 and over by mid-April, and all adults by the end of July."