The withdrawal comes after representatives of the ruling Conservative Party opposed the idea, saying it would burden businesses and violate human rights.
Health Minister Sajid Javid clarified that the decision could be changed in the event of another sharp increase in the number of people infected with coronavirus.
The idea of a vaccination passport is not popular in the UK, where citizens are generally not required to carry identity documents.
On Sunday in the UK, 56 deaths were reported with COVID-19, one hundred less than on Saturday. 29,173 new cases were registered, compared to 29,547 on Saturday, Reuters reported.