The hadith on this matter is this:
Narrated by Abdullah ibn Umar RA ; Abdullah ibn Amr RA:
Allah's Messenger said, "If anyone drinks wine Allah will
not accept prayer from him for forty days, but if he repents Allah
will forgive him. If he repeats the offence Allah will not accept
prayer from him for forty days, but if he repents Allah will
forgive him. If he again repeats the offence Allah will not accept
prayer from him for forty days, but if he repents Allah will
forgive him. If he repeats it a fourth time Allah will not accept
prayer from him for forty days, and if he repents Allah will not
forgive him, but will give him to drink of the river of the fluid
flowing from the inhabitants of Hell." (Thirmidzi)
Note that this hadith deals particularly with the wilful
consumption of alcohol. I'm not sure about how non-halal meat gets
into the picture.