Jellybear, as someone who has had dealings with builders, I can say that you have approached this problem in completely the wrong way. In the first place you really ought to have gone and spoken to your neighbour long before you applied for planning permission. You should have discussed with her in detail what it was you were planning to build and whether it was going to affect her in any way because of the closeness to her property.
What you have done here ( unless I have missed something ) is apply for planning, and I presume you put up a site notice, and got moving on the build without one bit of consideration for your neighbour. If you knew that you needed access to her property surely that was the first thing to secure before anything else.
I have had several instances where builders just bulldoze their way (excuse the pun ) without a thought for anyone but themselves. There is no prior discussion or warning of intending to build and sometimes you would need a magnifying glass to see the site notice or else it is stuck in a hedge where it can't be seen.
It's no wonder your neighbour has dug her heels in and is refusing to budge. Lessons can be learned here for the future. You make it sound now as if you are doing her a favour in building her a wall. Maybe she would prefer the hedge, as it probably gives her more privacy. It is you now that needs the favour, not her. If I were you I would go and apologise for not consulting her earlier and hope that she has a change of heart.