Mr Johnson met with Mr Hancock, Rishi Sunak and Michael Gove last Sunday, when they decided to delay reopening until July 19 amid the spread of the new variant first detected in India.
The study showed that the Pfizer and AstraZeneca vaccines were more effective on the Delta variant than they were on previous strains.
According to the Sunday Telegraph, the data was not included on briefing papers sent Mr Johnson, Mr Sunak and Mr Gove in advance of the Freedom Day meeting last Sunday.
They only received the data at 3pm on Sunday, so close to their meeting that it was not meaningful to their discussion.
Speaking to the newspaper Steve Baker, the deputy chairman of the Covid Recovery Group of Conservative MPs, said: “Either Matt Hancock thought this data was insignificant or he thought it should be withheld from the Prime Minister and other key ministers.
“Either way, the mind boggles at what conversation must now be necessary with the Prime Minister, and I feel confident it will be a matter of interest to my colleagues on the relevant select committees. If Matt Hancock was deliberately withholding relevant information, what was he trying to gain?”
Mr Johnson was forced to publicly back Mr Hancock last week after former top aide Dominic Cummings released a series of text messages from the PM in which he called the health secretary “hopeless”.
The data on vaccines will boost hopes that Mr Johnson will not wait until July 19 to reopen, but will do so on July 5.
A Government source insisted that “equivalent data” to the PHE study was shown to senior ministers.
The “equivalent” data was said to have been drawn up by Sage’s Scientific Pandemic Influenza Group on Modelling (Spi-M) and to have included similar figures to the PHE’s findings on the efficacy of the vaccines.
The source said: “When the decision was made to delay, ministers knew that the vaccines work. That is why we are buying more time to get more jabs in arms.”
A Department of Health spokesman said: “Information which was provided by PHE was shared across Government before the meeting.
“Analysis and work on the scientific paper continued over the weekend before it was published as soon as it was ready on Monday.”