I was just listening to a programme on Elgar and not paying complete attention missed the title of a beautiful poem by his wife.I will try to get...

I think you are speaking of
a poem from a collection called the Lute Song. The writer of the
lyrics is C. Alice Elgar, the daughter of Henry Roberts; she was born in India.  She
marries Elgar and contributes a number of her poems to his music. Her influence on him
was very strong as she becomes his inspiration and
partner.

I am guessing the poem in question is
"Love Alone Will Stay," written in three stanzas of three lines with each line rhyming
within the stanza.  I include it below.  It is a simple, yet beautiful verse, and if you
find the music, you may also find that this is the work in question.  It comes from a
song cycle originally called Sea Pictures, and renamed
Lute Song.

According the the
Elgar Society:

readability="10">

"This collection of five poems [Lute Song] set
to music by Elgar has been criticised on a number of pretexts : the poems now seem
rather dated; apart from the rather superficial link of the sea, there is no thematic
interconnection between the poems, so that the cycle as a whole lacks a coherent
structure; and Elgar's settings make little attempt at a grand portrayal of the sea as
other composers have successfully
attempted.

readability="12">

"Fortunately, the listening public pay little
heed to such criticisms, for the song cycle remains one of the most popular of Elgar's -
and indeed any composer's - vocal works. The second song is of particular interest. ....
Elgar set the poem some three years earlier, publishing it separately under the title
Love Alone but later incorporated it
into the song cycle, in which it is undoubtedly the most charming of the five
songs."

Alice Elgar did,
however, write other pieces used by her husband, including: "O Happy Eyes" (1889), "The
Snow" (1894), and "Fly Singing Bird" (1894).

readability="12">

"Elgar honed in on “Love Alone Will Stay" [Lute
Song], a short song for piano and voice that he had composed two years earlier. ... his
wife, Caroline Alice Elgar, had written after a long-ago holiday on the Italian island
of Capri. After she made slight adjustments to the text, he orchestrated the song as “In
Haven.” Alice’s revised poem gave rise to the underlying maritime metaphor that links
Sea Pictures...."

Here is the
poem; I hope this is the work for which you were
searching:

readability="23">

Closely cling, for winds drive fast,

Blossoms perish in the blast,

Love alone will last.

Closely let me hold thy hand,

Storms are sweeping sea and land,

Love alone will stand.

Kiss my lips, and softly
say,

"Joy may go and sunlit day,

Love alone will
stay."