Baby pigeon found in the front garden, what to do?!?

So, early this morning we happened to find a young pigeon under my grans car.
It looks as if it had been there all night.
We had to go out today so we left the pigeon out in the garden just inside this rabbit run, with an open side so it can get out.
We came back 3 hours later and it was still there.
I'm afraid to leave it in the front garden because there are cars which come zooming up our road and also there are a lot of cats around. We can't put it in our back garden because we have dogs.
The pigeon has probably only just left its nest, as a new fledgeling, because it doesn't seem to be able to fly yet.
It's in good health and there doesn't seem to be anything wrong with it.
But what should we do?
There are cats, cars and it gets quite cold at night.
What to dooo?
My gran was thinking about calling the RSPBA but... I'm not sure if they would do anything.
Thanks!
 
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