I think there are different kinds of loneliness, if that's any help OP.
I have two very young DCs but am single mum and experience the same phenomenon of not being able to meet up with other families and married friends at weekends as you do. Generally I find the weekends can be a bit lonely and stressful as the only contact is with my two small children, only one of whom can talk abit. Sometimes if I do meet up with friends, afterwards I feel even more lonely because there's no constant presence of another adult any more...
I used to have a different kind of loneliness before I had the children, which was combined with a definite existential angst of not knowing what I was doing with my life really. Now i have children (as a single parent, never had a partner) I do feel my purpose in life is to care for them.
I am abit of a planner, so if I'm not happy in the present, I spend loads of resources making hypothetical plans for the future...even if they don't come off in the end, it passes the time, generates hope, excitement, etc.! The children are in bed by 8 every night and I never leave them then (so haven't been out after this time since the eldest was born nearly 4 years ago), that can be my lonely time as there's no-one to share stuff with: but I find ways of sharing, emailing news to faraway friends, planning etc. Sometimes feel sad but, like you, don't want a partner.
I always used to have Xmas on my own and do now with the children. I used to go away, mainly to have a holiday booked as so many people would offer I go to theirs and I would find it very uncomfortable if I did! It's totally different now with children.
Given you've posted on Mumsnet, are you thinking of having children, perhaps? It's possible without a partner...