Blamire scored a try for the England U20 team against Italy during the 2017 Six Nations Under 20s Championship and also featured in the final game against Ireland as England completed the grand slam. He was also a member of the squad that finished runners up to New Zealand at the 2017 World Rugby Under 20 Championship. In June 2021 he was selected by Eddie Jones for the senior England team and on 4 July 2021 scored a try on his debut against the United States at Twickenham. The following weekend saw him score a hat-trick of tries on his first start in a victory against Canada.