Cope was born in Erith in Kent (now in the London Borough of Bexley), where her father Fred Cope was manager of the local Department store, Hedley Mitchell. She was educated at West Lodge Preparatory School in Sidcup and Farrington's School, Chislehurst in Kent (now also in London). Following her graduation from St Hilda's College, Cope spent fifteen years as a primary-school teacher. In 1981, she became Arts and Reviews editor for the Inner London Education Authority magazine, Contact. Five years later she became a freelance writer and was a television critic for The Spectator magazine until 1990.
Four collections of her adult poetry have been published, Making Cocoa for Kingsley Amis in 1986, Serious Concerns in 1992, If I Don't Know in 2001, and Family Values in 2011. She has also edited several anthologies of comic verse and was a judge of the 2007 Man Booker Prize.
In 1998, she was voted the listeners' choice in a BBC Radio 4 poll to succeed Ted Hughes as Poet Laureate. When Andrew Motion's term as Poet Laureate came to an end in 2009, Cope was again widely considered a popular candidate, although she believes the post should be discontinued. Carol Ann Duffy succeeded Motion as Poet Laureate.
Cope was appointed Officer of the Order of the British Empire (OBE) in the 2010 Birthday Honours. In April 2011, the British Library purchased Cope's archive including manuscripts, school reports and 40,000 emails, the largest email archive they have bought to date. The papers also includes 67 poetry notebooks and unpublished poems. Cope commented "I wanted to find a good home for my archive. The timing was dictated because we had to move home, so we needed some money to buy a house, and the space. So this was the moment. I asked Andrew Motion what I should do, and he told me someone to approach at the British Library. I wasn't sure they would want it, but they did." When the collection is catalogued and organised, the archive will be available to researchers.
Despite her slight output, her books have sold well and she has attracted a popular following with her lighthearted, often comical poetry, as well as achieving literary credibility winning two awards and making an award shortlist over a fourteen-year period. She has a keen eye for the everyday, mundane aspects of English life, especially the desires, frustrations, hopes, confusions and emotions in intimate relationships. Dr Rowan Williams is a well known fan of her work, writing that: "Wendy Cope is without doubt the wittiest of contemporary English poets, and says a lot of extremely serious things".
Three haiku from Making Cocoa for Kingsley Amis, where they are presented as being written by the (fictional) Tulse Hill poet Jason Strugnell, were set by the composer Colin Matthews in 1990 as Strugnell's Haiku.
Some of her poems are written in the persona of a struggling male poet, Jason Strugnell, a slightly seedy figure from Tulse Hill. She displays her talent for parody with targets ranging from the sonnets of Sir Philip Sidney:
My true love hath my heart and I have hers
We swapped last Tuesday and felt quite elated
But now whenever one of us refers
To 'my heart' things get rather complicated.
In April one seldom feels cheerful;
Dry stones, sun and dust make me fearful;
Clairvoyants distress me,
Commuters depress me—
Met Stetson and gave him an earful.