Some of them are "free range" and some of them presumably are not, so I suppose "naturally reared" is a euphemism for "not battery turkeys".
According to this website the battery turkeys are fat and feeble and can't move much because their legs will collapse. They sound a bit like the avian version of hippy: http://www.hartstraditionalturkeys.co.uk/ourturkeys.html
I looked on the sainos website and they have a few turkeys: http://www.sainsburys.co.uk/shop/gb/groceries/get-ideas/christmas2014/turkeyguide-2014
Some of them are "free range" and some of them presumably are not, so I suppose "naturally reared" is a euphemism for "not battery turkeys".
According to this website the battery turkeys are fat and feeble and can't move much because their legs will collapse. They sound a bit like the avian version of hippy: http://www.hartstraditionalturkeys.co.uk/ourturkeys.html