Magpie's attacked young bird. What to do? (1 Viewer)

I'm in a fluster.
A huge commotion was going on in my garden half an hour ago. Birds were squawking from all around. I ran outside to see a magpie on my garage roof. I scared it and it took off - dropping a baby bird.
I assumed it had killed it, but on reaching it, it was still breathing. I could see an injury on it's face and it looked like it had no claws on a couple of it's toes, but the toes weren't bleeding.
I couldn't just leave it there and carefully lifted it down. It is cold outside today, so rightly or wrongly, I have made it a 'nest' in an old straw hat and am trying to keep it warm. It is still alive, but what should I do for it, please?
I have 'facebooked' a local wildlife rescue, but had no response as yet and am without transport to take it anywhere.
I don't know if it is a young starling or blackbird. It seems to have a largish, wide beak and has it's fluffy feathers and a stumpy tail.
Thanks.

** UPDATE ** Sadly the little bird has died.

Just seen this - and I was about to say that there was probably little you can do and the trauma, if not the actual injuries, is usually fatal.
Nature in action - magpie has to eat and feed its young too!
Mick

Sorry to hear the little bird died, but well done for doing your best to help it.

Unfortunately, it is just nature and like the post above says, the magpie has to eat too. Hopefully other birds in the nest fledged