As reported by the BBC:
England’s NHS app will be available to use as a vaccine passport from Monday, the government has said – but only for those who have had both doses of the jab.
A paper version will also be available – by calling 119 but not through a GP.
Both will be available from Monday, 17 May, when the ban on foreign travel is eased.
You can download the NHS App here https://www.nhs.uk/nhs-services/online-services/nhs-app/
The NHS app is separate to the NHS Covid-19 app, which is used for contact tracing.