[13] On 29 May 2020, Parkinson was named in a 55-man group of players to begin training ahead of international fixtures starting in England following the COVID-19 pandemic.

[14][15] On 17 June 2020, Parkinson was included in England's 30-man squad to start training behind closed doors for the Test series against the West Indies.

[16][17] On 9 July 2020, Parkinson was also included in England's 24-man squad to start training behind closed doors for the ODI series against Ireland.

[23] In the final ODI of the 2021 Pakistan Tour of England, Parkinson bowled Imam-ul-Haq, placing the ball in the rough, and generating a large amount of turn.

Parkinson made his Test debut on 2 June 2022, for England against New Zealand, as a concussion substitute replacing Jack Leach.