As a person who has raised and lived with both a red squirrel and a grey squirrel, I am emminently qualified to stake out a position here. Not to mention being one of the last crackers in my neighborhood.
My avatar image is of my little red (RIP).
There's a T-shirt that comes to mind regarding this situation.
http://www.tshirthell.com/shirts/products/a355/thumb_ltd_a355.gif
British red squirrels: little pussies should have fought harder.
Now I have to say that I'm kidding here. I'm of mixed Euro and Native American Indian lineage so...
North American Red squirrels kick the crap out of North American Grey squirrels despite being nearly half the size of the greys. This shows the Brit Reds are indeed pussies.
OK, I'm kidding again.
I love them all, and only non-lethal means should be used to preserve the UK Reds.
Each life of the squirrel, native or not, means as much to it (him or her), regardless of it's color. It seems unfair to kill an individual grey just because the group he's a member of is outbreeding the other group. The arguement for lethal means could be just as readily applied to the white people of the US who are rapidly being outbred by browns and blacks. And there's a phrase that describes that: Nazism. It's not fair for humans, nor for squirrels.