If it straddles the boundary, then they can, but they have to serve Part Wall Act notice.
If it does not straddle the boundary then if they try to key into it, it is trespass and you can apply to court for an injunction to stop them.
What you could do, it is important to their build, is asked them for money for consent. The amount is up to you, there is no fixed sum set anywhere in statute.
Can I clarify anything for you?
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