The first of seven children, she was a child performer and wrote, produced, directed and starred in her own shows for many years. Famous for her catchphrase: "She knows you know" which stemmed from her music hall days, Baker is probably best known for her role in the Granada/ITV television series Nearest and Dearest (1968-1973). Her character Nellie Pledge (co-owner of a Lancashire pickle factory, Pledge's Purer Pickles), was ideally suited to her talents and she was cast opposite the comedian Jimmy Jewel. The two actors notoriously hated each other and repeatedly tried to stitch each other up in the often one-take shooting. This included corpsing and trampling over each other's laughs. Between shoots they would only speak to each other through a third party, even though they sat only feet away. A theatrical version appeared in 1972 (produced by Hammer Films), followed by a near sequel Not On Your Nellie (London Weekend Television/ITV, 1974-1975), in which she played a similar character (Nellie Pickersgill) who moved from Bolton to London to take charge of her ailing father's pub. Both of Baker's "Nellie" characters were renowned for their malapropisms, which were used to great comic effect.
For her role in Nearest and Dearest, she received special recognition at the 1969 Australian World Television Festival.
In 1978, aged 73, Baker recorded a spoof version of "You're The One That I Want" (from the musical Grease) with fellow British comedian Arthur Mullard. Released shortly after John Travolta and Olivia Newton-John's version had spent 9 weeks at the top of the UK singles chart, Baker and Mullard's version was also a hit, though a more modest one. The single peaked at no.22, though the pair did make an infamous appearance on Top Of The Pops. "...and it was a complete disaster and the next day we went from 30,000 records; in two days we went to 250. It just absolutely killed it stone dead" so said the record's producer Kenny Lynch of their appearance. The B-side to the single was their version of the 1976 Brotherhood of Man hit "Save Your Kisses for Me".
In her last years Baker suffered from Alzheimer's disease. She died at a retirement home in Surrey in 1986, aged 81.