Viewers praised the actress's performance as the Victorian landowner, prolific diarist and would-be coal baron Anne Lister following the first episode.
Written by Happy Valley's Sally Wainwright and co-starring Sophie Rundle as Anne's love interest Ann Walker, the show has finally arrived on British screens after getting a head-start in the US on HBO.
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There is high praise for Doctor Foster star Suranne Jones in her new role:
Fans also appreciated how Wainwright's drama portrays Anne Lister's sexuality and love life.
The 2019 Bafta TV Awards may have only just taken place, but fans reckon Suranne Jones is already a dead cert for next year's awards ceremony:
Gentleman Jack continues on Sundays at 9pm on BBC1