Does the crown of next door's tree hang over the top of the east border? What plants have you used there? How close to the fence are they planted - actually a photo or two would be helpful.

Sounds like they are reaching for more light.

Also you may have had a strong wind at some point which can do this.

Right, to answer questions. No, Bamboo, the crown of the tree doesn't overhang the garden. Yet! One of the photos shows the huge goat willow in the background of the house next door where the cherry is.
Stera, although we are surrounded by houses we do get fairly strong winds.

My instinct says Bathurst is right but I'm attaching photos though you may have to enlarge them - I apologise for that. The tallest Nicotiana are tied up to the fence, the Just Joey rose is also propped up. The Eryngium, which is in front leans by about 45 degrees like most of the others. The Japanese Anemones and the Echinops both lean forwards by nearly 90 degrees but that may be due to the shed on one side and the house wall on the other. There is also a Yarrow there which, being tall, is leaning so much that it's almost touching the ground.

Any clarification would be welcome, as would a solution if there is one.

Thanks for the photos, but they're not terribly helpful, all they show is leaning plants relatively close up; a photo taken further away showing most of that area is what would help.
Its probably safe to assume that area does not get sufficient light, so really it needs to be planted up with shade lovers rather than those that require sun, especially if the border is quite narrow (under 5 feet from front to back)

One pic shows a large wall covered with ivy at the back of the border - that would easily cause a lean as I'd imagine the border doesn't get sun in the first part of the morning?.

See my next post with further pictures.

There is no ivy, Stera. It’s possibly the Montana you can see.
I agree the pictures aren’t helpful though they would have been if you could have viewed all six of them.