McGeever was trained at RADA, and became diabetic at age 19.
McGeever became pregnant in 2001, but developed pre-eclampsia. Her son Felix was born two months early; he spent some time in a special care baby unit. At the age of four months, he suddenly became very ill, having problems with his heart and lungs.
During her son's illness, McGeever also became ill due to the stress - her kidneys stopped working, she had heart trouble, and diabetic retinopathy caused her to begin to lose her sight. Laser treatment was ineffective; five months later she was blind at the age of 32. Her son Felix died in January 2003, aged fifteen months.
She was given a kidney transplant in a successful 12-hour operation. Following her recovery, she contacted her agent in 2008 and suggested that she was ready to begin performing again, and would consider television.
She was spotted by production staff from the soap Emmerdale when she was appearing in a one-woman stage show where she talked about her life as a blind woman. They approached her with a view to creating an authentic blind character for Emmerdale, to be played by McGeever, who would also develop the part. She first appeared as former criminal Lizzie Lakely in Emmerdale on 28 April 2009, at the age of 38; Lakely is the first permanent blind character in a British soap. She is given her scripts as sound recordings, and has two government-sponsored assistants to guide her around the studios; they also guide her through the sets during rehearsals, and ensure continuity between recordings.
On 5 January 2010, McGeever appeared on the BBC Radio 4 programme In Touch, when she talked to Peter White about losing her sight. She revealed that she has a number of gadgets to assist her, including a CD storage system where audible labels can be recorded, a colour detector to assist with choosing a coordinating outfit, and a pair of long-armed oven gloves.
McGeever's sister Caroline Mitchell is a member of the Emmerdale writing team.