The Swindon-based firm will produce 170,000 A4 packs which contain 14 elements including posters, magazines and scratchcards.
"The charity sector is not one we have delved into much but corporate social responsibility is important to us," said ESP managing director Paul Bradley.
Although the value of the contract is undisclosed, ESP negotiated a reduced rate with the BBC. The firm has worked regularly with the corporation and last year produced Christmas cards for the Children in Need appeal, which this year takes place on 19 November.
The work will be carried out on ESP's Heidelberg Speedmaster 102 and Komori Lithrone 840 presses.
ESP has a workforce of 73 and its services include print, repro, design and fulfilment.
Story by Philip Chadwick
