I suffer with the same problem,my face has cleared up but my neck hasn't.
I thought that the skin on the neck was thinner than the skin on the face and thus you have to be more gentle with it.
I have used B.P on my neck for many years without much success.
Yesterday i visited my Derm who told me to stop using all of the products i currently use including my shaving cream and to switch to Dermol Lotion,it's a antiseptic moisturizer that you can use instead of soap and shaving cream.
She has told me to return in 10 weeks time,so maybe this stuff will take a while to work.
My old method of getting rid of spots basically entailed using harsh drying products,they did help with the spots but they have totally ruined the skin on my neck,it's red and sore pretty much all of the time these days.
Hopefully this lotion may be the answer.