Injured Wood Pigeon

Can anyone please help me with an injured wood pigeon?

I am in Lancs WN8.

Looks like a damaged beak but it won't fly, it just runs when i approach it.... im worried its going to be cat food tonight, i dont have a cat but neighbours do.

I have fed it soggy bread, cheese and garden peas. It did appear to pick at.

Its defo injured as it didnt fly away when i was mowing the lawn. It just walked to opposite side