Do I 'own' x & y or y & z?

If it is x & y then presumably I need permission from the owner next
door to repoint wall 'z'.

You own x & y.

You have a legal right to enter the property next door to maintain x,
although you have a duty to do so reasonably. If your neighbours refuse, a
court will grant an injunction allowing you to enter.

Your neighbour owns z.

Your neighbour, unless they are mentally defective, will be delighted to
have you repoint their property, provided you DON'T USE CEMENT!!!!!

If you destroy a neighbour's wall using cement based mortar, you will
probably be liable for the damage, which could run in thousands. If you are
doing it yourself, then you can make up the right lime mix. If getting
someone in, make sure they know about lime. You probably want a builder
specialising in older properties.

Christian.