Queen Elizabeth has been played by numerous actors over the years — three in Netflix’s The Crown alone. But tracking not far behind when it comes to onscreen depictions of major British figures is former prime minister Tony Blair. Among the names to have stepped into the shiny brogues of the divisive politician are the likes of Damien Lewis, Robert Lindsay, Toby Stephens, James Larkin, Ioan Gruffudd, Stephen Mangan, Harry Enfield and Pierce Brosnan (as a version of Blair in Roman Polanski’s The Ghost Writer). Michael Sheen has also famously played Blair three times.

Joining this illustrious list is Bertie Carvel, the star of stage and screen who joined The Crown for its final outings in seasons five and six. While he’s mostly a supporting bystander in season five, the sixth and final season of Netflix’s hit royal drama — which centered its first four episodes, now streaming,...