This line comes from the middle stanza of the poem For the Fallen by Laurence Binyon (1869-1943).  The poem was first published in The Times on 21 September, 1914, a few weeks after the start of the First World War. The whole of this middle verse is traditionally recited as part of Remembrance Day services throughout the United Kingdom.

 
At the time of the publication of the poem, Binyon was head of the British Museum's section of Oriental Prints and Drawings.  He was, therefore, in a reserved occupation and, as he was in his forties, considered too old to serve in the armed forces.  However, he volunteered for the Red Cross and spent much of his annual leave during the war working as a medical orderly in France.

The verse recited at Remembrance services throughout the country is as follows:-

They shall not grow old as we that are left grow old:
   Age shall not weary them, nor the years condemn.
     At the going down of the sun and in the morning
                          We will remember them.

If you are interested in reading more about the poetry of the First World War click here for details of how to visit the Department of Printed Books.

Sources:
The winnowing fan: poems on the Great War by Laurence Binyon (pub. Elkin Mathews, London, 1914)
Laurence Binyon: poet, scholar of East and West by John Hatcher (pub. Clarendon Press, Oxford, 1995) ISBN 0-19-812296-9