People vaccinated in England who have had a full course of the COVID-19 vaccine can now demonstrate their COVID-19 vaccination status for international travel and for events. NHS Digital has produced a guide which you can find here NHS Digital website.
You should also be able to view your vaccine status on the NHS app or via the NHS desktop app. We would recommend downloading the NHS app as it has many other features including checking your medical records, requesting prescriptions and get general health advice. Here is the link to the app NHS app