Curtis was born in London in December 1923 to Eastern European Jewish immigrants Ada and Manny Brown. Her mother and aunt operated a millinery shop. Curtis was raised in Upper Street, Islington. When the Second World War broke out, she was evacuated to Somerset and came into contact with the Workers' Educational Association. The association helped to form her independent socialist outlook which had its origins from her father and led to Curtis being curious about miners collecting money on the streets during the 1926 General Strike. Curtis meet naval officer Gerry Curtis in 1943 and after the two began dating, they became involved in the running of the left-wing progressive Unity Theatre. The two married the following year and established residence in Finchley, where Curtis joined the Communist Party.