Hi
I was in a similar position to you. I contacted the SS adoption team for advice and was told that I had to seek the biological father's permission
.
My DS was 7 at the time, has still never met his father (he's 13 now) and my DH has been his dad since DS was 13 months old.
The SW asked why DH wanted to adopt him. I told them. It was because he is his 'dad', we had had another child and wanted our family to be protected in law if anything happened to me and to know that he was part of our family.
I'll never forget the patronising smug reply "yes, but he already has a family, doesn't he?" meaning his paternal family who've never made any effort at all despite my early efforts!
She said that we had to put posters up/adverts in the newspaper/make whatever efforts we could to make contact with his father to seek his permission, but we should also be aware that doing so doesn't often result in permission being given but can rouse the absent father's curiosity and we needed to be aware that he might decide he wanted some involvement afterall.
So we decided not to bother. 
So that was our experience of contacting SS. I don't know what a solicitor would advise, probably similar. Oh and we were also told that DH would have to undergo a SW assessment to assess his suitability to adopt. 
There's more info here
Good luck