BBC sketch show It's Kevin and in Psychobitches on Sky Arts. She appeared in an episode of Inside No. 9 as a stage manager. Davis created, wrote and starred in Hunderby, which aired for two series on Sky Atlantic in 2012 and 2015. For Hunderby, Davis won the BAFTA TV Craft Award for Writing – Comedy. At the 2013 BAFTA TV Awards, Hunderby was nominated for Best Scripted Comedy and Davis was nominated for Best Female Performance in a Comedy Programme. At the 2012 British Comedy Awards, Hunderby won the awards for Best New Comedy and Best Sitcom. In 2014, she cowrote and starred in a pilot for Channel 4 called Morning Has Broken, about a struggling daytime TV host. A full series of Morning Has Broken was commissioned but ultimately did not happen. She starred as an eccentric mother in the comedy short film The Bird. 2015–present: Camping, Sally4Ever and podcast In 2015, Davis and Marc Wootton created and starred in BBC Radio 4 comedy series Couples, about couples in therapy. It was reported in 2015 that Davis had been commissioned for a new series, Robin's Test, which was later renamed Camping. In 2016 Davis wrote, directed and starred as shallow nymphomaniac "Fay" in Camping on Sky Atlantic. This was her directorial debut. At the 2017 BAFTA TV Awards, Camping was nominated for Best Scripted Comedy. In 2017, Davis was featured in the Paul Thomas Anderson film Phantom Thread as Lady Baltimore. In 2018 Davis wrote, directed and starred in the comedy television series Sally4Ever on Sky Atlantic and HBO. Davis plays the character of Emma, who is having a lesbian affair with a woman called Sally, who is having a midlife crisis. At the 2019 BAFTA awards it won the award for Best Scripted Comedy and Davis was nominated for Best Female Performance in a Comedy Programme. She also appeared in the film Fighting with My Family. Davis launched the podcast comedy Dear Joan And Jericha with comedian Vicki Pepperdine in 2018. The series has 27 episodes as of November 2021. Davis and Pepperdine published a book on the back of the podcast, Why He Turns Away: Dos and Don'ts From Dating to Death. Davis played socialite Maureen, Marchioness of Dufferin and Ava, in BBC One historical drama A Very British Scandal, which premiered on BBC One on Boxing Day 2021. In 2022, Davis appeared in two episodes