There is no legal convention, it is a legal myth, where the property on the left is responsible for one boundary and the property on the right the other. The same applies when one property is higher than the other.
If one property was built later than the other, would be the responsibility of the later addition normally.
If the properties were built at the same time, then it’s a joint responsibility.
If one party will not agree to pay half of the cost of any remedial work, then the other party will have to do the work, pay for it and then seek the cost from the nonpaying party, through the Small Claims Court if necessary.
Can I clarify anything else for you?
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We can still exchange emails. Best wishes. FES.
PS assuming there is no mention in the deeds of who is responsible for which boundary.