Joseph, 64, is a winner of the Forward Poetry Prize and "Warning" has been in a number of collections. Nevertheless, it is a surprise that a relatively little-known poet should be holding prime position.
Her first book of poems was published in 1960 and immediately won an award, as did her second collection and subsequent books. The Times Literary Supplement has described her best poems as revealing "a world living in the clutches of disappointment and mortality, but open to the possibility of intense delight in minute but dazzling particulars of nature and in rare acts of human kindness".
Despite the BBC's attempt to attract the young and widen the definition of poetry, including rock lyrics, the top three are all poems about growing old. The only pop lyric in the top 20 is John Lennon's "Imagine".
When I am an old woman I shall wear purple
With a red hat which doesn't go, and doesn't suit me.
And I shall spend my pension on brandy and summer gloves
And satin sandals, and say we've no money for butter.
Last year Rudyard Kipling's "If" won the BBC poll for the nation's favourite poem ever. This year the poll, aimed to coincide with National Poetry Day today, was limited to poems written in the last 50 years.
Daisy Goodwin, producer of The Nation's Favourite Poem, to be broadcast tomorrow night, said: "Love and sex and the fun things are dealt with by pop music but the really awkward things, when you're looking for solace, remain the province of poetry."
Other poets, such as Larkin and Betjeman, have polled more votes than Joseph, but the votes have been split between different works.
r John Fuller won the fifth annual pounds 10,000 Forward Poetry Prize with his collection "Stones and Fires".
Daily Poem, page 11