The wall dividing you from the adjoining house is owned by both of you jointly and, although she or he can't stop you, it is important for them to know what's going on and that you're not damaging anything.
Normally it's just a question of you handing over a "party wall notice" and an "acknowledgement form" for them to sign and return.
Some might exercise their right to use their own surveyor at your expense to check things out, but most are happy to go along with ours.
There's more about this if you click practicalities above and you can click here for a draft of a party wall notice.