NHS data shows the number of cases has fallen from a high of 635 a day at the start of this month to 367 last week.
The trend came despite a rise in the total numbers of Covid sufferers in hospital from around 25,000 to 37,000 over the period.
On Wednesday night, Sir Patrick Vallance, the chief scientific adviser, said early findings from Israel – which has already given first jabs to almost a third of its population – suggested they could cut rates of transmission by around 60 per cent.
However, Sir Patrick told a Downing Street briefing that he would be "extremely cautious" about making an assessment of the impact of the vaccines on transmission until there was "proper data" to assess.
Boris Johnson said proof about the impact of vaccines should emerge by the middle of February. A study by Public Health England (PHE), tracking 40,000 health workers – including those given jabs early in the vaccination programme – is expected to report its findings next month.
NHS staff were among those offered Covid jabs when the vaccination programme began in December, with a concerted push at the start of this month after the AstraZeneca jab became available.
Health and care workers were among more than 400,000 under-80s to have received jabs by the turn of the year, a number that rose to more than 1.8 million by mid-January.
Cases of probable hospital-acquired infection of Covid have been a major concern throughout the pandemic, with more than 11,000 such cases in the four weeks ending January 5. Government scientists have repeatedly expressed concern that the spread of the virus in hospitals is seeding infections in the community.
On Wednesday, Whitehall sources said trends in recent weeks gave some hope that vaccines may be beginning to have an impact on transmission, and PHE has embarked on research of thousands of healthcare workers in order to fully assess the effect.
Government scientists have repeatedly stressed that they do not yet know the impact of the vaccine on transmission of the virus, urging those who have the jab to keep following social distancing rules.
But Government sources said the recent drop in cases of "probable hospital acquired infections" – those where a diagnosis of Covid is made at least seven days after admission –gave some grounds for optimism.
One said: "We know that the vaccines have some impact on symptoms, so the hope is that this will translate into a reduction in transmission, but we don't yet have the evidence. It could be that we are just beginning to see some of these changes being played out in hospitals now growing numbers of staff have had their first jab."
However, experts said other policies, such as lockdown rules and the wider rollout of NHS staff testing, may also be having an impact on transmission rates.
The latest surveillance data from Imperial College suggests that infection rates are stable, with one in 64 people infected between January 6 and 22. However, scientists said the data showed some signs of a downtick, saying that was "really good news".
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