It need to become socially unacceptable to own a gun.
I disagree. It's not socially unacceptable in the UK. I know several people who own guns. I also know that these guns are subject to license and periodic inspection to ensure they're properly stored, and the owner is subject to background checks and license renewal.
It's the ludicrous ease with which people can acquire firearms (registered and unregistered) in the USA that bewilders me.