Roberts lives with her husband and two children, a daughter born in 2010 and a son born in 2013. She met her husband in Cardiff in 1997 when she was a medical student and he was an archaeology student. She is a pescatarian, an atheist and president of Humanists UK, beginning her three-year term in January 2019. Her children were assigned a faith school due to over-subscription of her local community schools; she campaigns against state-funded religious schools, citing her story as an example of the problems perpetuated by faith schools.