I think the type of loneliness that you're describing is a distinctly partner loneliness, rather than a "friend for coffee and a chat" type of loneliness. I'm living alone now, focused on my recovery, working a job I love, have friends that I do things with, active in AA, and still, late at night, I just want someone to snuggle with on the couch, someone who cares how my day went in a different way than a friend, someone who will rub my feet if they are tired.
It comes up for me at interesting moments. I notice it when I need to put an emergency number on something at a doctor's office. I have friends that I put, but it isn't the same. I think it is a loss of the sense of "belonging" to someone.
I haven't always had that "belonging to" within relationships either, but glimpses, and in some relationships a surety that should there be a car crash, there was someone who would be sitting bedside, concerned, adult, mine.
I don't have any biological family living near me. Good relationships with bio-family might take some of the "belonging to" edge off, I don't know.
I do know that I'm not ready for dating quite yet. Still working on enough internal stuff that I am afraid love will distract me from.
In the interim, I'm contenting myself with "connecting with" fellas who might someday be relationship material, but as friends, without the flirting or the physical. I've realized that I move very quickly into relationship and sexuality with men, and then get "stuck" with all their dysfunction and addiction - much of which I would have noticed and would have influenced my decision-making if I had spent an ample amount of time with them first, as the strangers-becoming-friends that people actually are at some point. I typically do strangers-becoming-partners, and that has not worked for me.
I'm also taking care to make sure that I get a fair amount of nurturing touch from other sources - I get regular massage and I hug both men and women a lot at aa meetings. It isn't quite enough, but I'm accepting that it is where I am right now. My bed is vast and quite chilly at night when I go to sleep, and I simply don't like that. I've made a vow though, that the next person who warms my bed is going to love me and be kind to me and want "mutual belonging" as I do.
I've actually considered buying a stuffed animal toy to sleep with, but keep chickening out, because that just feels a little too "inner child work" to me. It keeps reappearing as an idea though, so I may just have to follow through...