If the wall is solely in your ownership, a neighbour generally needs your permission to attach fixtures such as trellis, wiring, or a shed to it. If ownership is shared or unclear, both parties' consent is usually appropriate before either side makes attachments or alterations.
Attaching something to a boundary wall, such as trellis, netting, a satellite dish bracket, guttering, or a lean-to structure, generally requires the consent of whoever owns the wall. If the deeds and evidence show the wall belongs entirely to you, your neighbour does not have an automatic right to fix anything to it, and doing so without permission could be treated as trespass or interference with your property.
Where ownership is shared, for example a genuine party wall, both owners typically need to agree on alterations that could affect the other's use or the wall's structural integrity. Even minor-seeming attachments can cause damage over time, such as damp ingress from fixings, or can affect the wall's appearance and stability, so it is reasonable to expect to be asked first regardless of how trivial the item seems.
If a neighbour has already attached something without asking, it is best to raise it directly and request removal or retrospective agreement, keeping a record of the communication. Where the item causes damage or the neighbour refuses to engage, further steps may include a formal letter, mediation, or legal advice, particularly if there is a pattern of unauthorised interference.