Strengthening Garden Wall

[AnniO]

I have a very old garden wall marking one of the terraces in my garden. You can only access one side of it. I am trying to attach a fence to the top of this wall. I previously fixed it to the top layer with bolt down fence posts and the top layer of bricks came away with strong wind. The fence was willow lattice panels between four 6 foot fence posts.

I would like to reattach the fence to the wall using the bolt down fence posts again but i am worried that another layer of the wall will again come away.

The layer that fell away was not part of the original wall it appears to have been added later (at least 12 years ago) but i don't think it was done particularly well. How can I ensure the wall is strong enough to support the fence posts?

Any help would be gratefully recieved as i really don't want to have to go through fixing it to the wall only for it all to blow over again :(