M....you are not alone...completely, anyway. My daughter, also 8, is pretty much the same. However, I am married and we also have a 3-year-old son. I did separate from my husband for about 10½ months, back in 2006, right after my son was born, but we got back together and we have all been together, happily, since.
My daughter follows me from room to room like I'm going to abandon her at any given second. The very rare times she decides to play alone in her room, she comes out every so often to look for me. If she doesn't see me, she immediately asks my husband, "Where's Mama??" She will not sleep in her own room unless I am in there with her, so her bed is in our room. When she showers, she wants me in there, but usually I can compromise and just leave the door open after she gets going. She doesn't follow me to the restroom (anymore), but will come peek in on me if I seem to be taking too long. She does NOT like for me to go anywhere without her, though. I play Bunco with a group of ladies once-a-month and she always cries because she wants to go or doesn't want me to go (some fits are worse than others). She does enjoy staying with grandparents or aunts/uncles without me, but that opportunity very rarely ever arises. I have no problem sending her off for school. She has friends there, and at daycare, but none outside of that, which I think has A LOT to do with this. I have made several attempts at finding her a friend that can come over and play or spend the night, just someone to hang out with other than me, but the parents just don't respond. She usually only has one MAYBE two friends to show up at birthday parties...one year NONE came. So, this year, she and I had a date to the nail salon for a mani/pedi. I try to do things like this with her once-in-a-while, leaving the boys at home so we can have some girl time, and it helps, I think.
Anyway, she is very clingy, too. But, I have never once considered counseling for her (us). I have just come to terms with the fact that this is who my daughter is and she just has some need to be close to me and I try to treasure that. I constantly assure her that I will NEVER abandon her, tell her all the time how much I love her, and try to have 'our time' periodically. I really believe that this is something that will work itself out as she gets older, grows in her self-confidence and is able to hang out with friends outside of school. I also think that any time apart is very healthy and helps her, even though the getting apart is the hard part sometimes. My return, or our re-union, is that proof that when I leave, I AM coming back to her. One day, I'll miss her always wanting to be with me, I am sure of that.