How long have you been with your boyfriend?
How old are the two of you?
Has he gone out with her alone before since you've been with him?
Has he ever been intimate with her? Where does he know her from?
Have you expressed concern? If so, what was his response?
This is dangerous ground he is on and in my opinion definitely something to be worried about. On one hand, he's been friends with her for a while, however when you get into a relationship, you have to re-evaluate your relationships with others. You have obviously invested yourself into this relationship emotionally and otherwise. You're helping him with his house, which is very thoughtful and shows a large commitment to him, but he's not necessarily returning that commitment.
He should never have told you not to come out with them for drinks. If he is in a relationship with you, then you are number one and everyone else comes after. The fact that he was in love with her makes the situation worse because as you said he will do anything with her that she asks. Not inviting you to dinner with them, not buying an extra ticket for you, them going for walks alone. You may feel like you don't have to worry about them having an affair but the reality is, they already are having an affair, it just may not be physical, yet. They are involved and invested with each other emotionally, and I'm sorry to say that's scarier than a physical relationship.
The botXXXXX XXXXXne is you can't be angry at her because she can only do what he allows her to do. Everything she does, he allows. He has to make a decision to make you number one in his life, you can't make that decision for him. Another thing that concerns me, she may have felt all this time that she had 'rights' to him, his feelings and his time, and may come to resent you. She may even find that she does have feelings for him once she realizes that the two of you are serious, or she could become jealous and try ways to get in between the two of you. Honestly it sounds like that is what she has already done and is doing.
I would talk to him about it, and give it time, but I wouldn't let this go on for too much longer, if within 4-6 months he hasn't made you more of a priority or the priority in his life and basically put this woman in her proper place, you may want to reconsider staying with him. The last thing you want is to stay and things don't change, and next year they are exactly the same. If you don't encourage a change, it's not likely he'll make one.
I welcome your thoughts, let me know if you want to talk more