It is a difficult situation, and I really sympathise with you, as I've been there and I didn't have the courage to deal properly with the situation.
I'd moved to a new area and I found it difficult at first to make friends, until about 6 months later when my DC started at playschool and school. Then, of course, I had the opportunity to meet with other mums. One in particular latched onto me. She lived only 3 doors away and we found ourselves walking home from the school together in the mornings. The second time we walked back I asked her in for coffee. She stayed all day, not leaving until it was time to walk down and collect the children from school. The next door she didn't wait for an invitation, but just followed me through my front door, and the pattern was set. This went on for weeks and I was longing for the school holidays, naively thinking I'd be free of her. No chance! She'd come in at some point during the day and I couldn't even get her to budge when I said I had to get dinner ready as my H would be home soon. She would even stay when he got in and started chatting to him. Unfortunately she didn't have to be home for her husband because he was away with the army. I would actually have to get the dinner plates out, and start laying the table, to make her go. But even then I still had to say, 'M, can you excuse us now please, as we are going to have our dinner.' I'm sure she would have happily sat with another cup of tea while we ate our meal. Heaven knows what her 8 year old son was doing all this time. She certainly didn't seem to care!
Eventually they moved away, but only after I'd endured her daily visits for over a year.
I wish you luck, LyndaW and more courage than I ever had