It is so fat that it obviously didn't gain enough height to either get onto the fence or off of the garden because it hit the garden fence. I think it's stunned as there are no obvious injuries, it is walking but it's making no attempts to fly. The dog is inside but not interested now anyway as if it doesn't move there is no chase.
I am terrified of birds so there is no way I can get it in a box or anything. What should I do? Leave it and hope it recovers before one of the neighbour's cats finishes it off. Open the back gate and let it out of the garden as it will have more chance of flight off the green at the back of the house and there are bushes and trees where it can take cover. Or something else?