Those given the first dose of either the Pfizer or AstraZeneca vaccines – and who became infected three weeks later – were between 38% and 49% less likely to pass the virus on than unvaccinated people, PHE found.
Health Secretary Matt Hancock described the study’s results as “terrific news”.
He has urged “everybody to get their vaccines as soon as they are eligible”.
In the study, protection against Covid was seen from about 14 days after vaccination, with similar levels of protection regardless of the age of cases or contacts, PHE said in a statement.
It added that this protection was on top of the reduced risk of a vaccinated person developing an asymptomatic infection in the first place, which is around 60 to 65% – four weeks after one dose of either vaccine.
Households are high-risk settings for transmission, meaning the study provides early evidence on the impact of vaccines in preventing onward transmission, PHE said.
Similar results could be expected in other settings with identical transmission risks, such as shared accommodation and prisons, it added.
University of Warwick epidemiologist Mike Tildesley said the findings were significant but pressed people to continue to take up vaccination offers.
“We need to remember these vaccines are not 100% effective either at preventing severe symptoms or at allowing yourself to be infected, but the evidence is suggesting they are providing at least some level of protection from passing the virus on if you do get infected,” he told BBC’s Breakfast.
