I have found a few alternatives (Link to Hope, Link Romania, Rotary Shoebox Scheme, Blythswood Care, International Aid Trust) but all of them are supported by Christian charities.
I accept it's not the most efficient way of helping families in poverty (the shipping cost being the main factor) but I think my DS would get more out of going to the shop to choose and buy items he would like himself for a less fortunate child, than just donating money to a local charity or buying an online gift.
I remember being told about 21st Century Child and OneChild OneWorld previously but I can't seem to find anything about them.