Q. The business next door [...].
Q. The business next door is extending along the party wall and is proposing to put up scaffolding in our yard. Are they allowed to do this? A. If it's a party wall you own it jointly and it cannot be altered without your consent. Works to a party wall often require a Party Wall Agreement, and the person proposing the works has to meet the costs of the other party. If you give consent, this agreement would include rights of access to put up scaffolding.
If you are likely to be affected by work on the foundations you should receive a notice a month before work starts. An extension built inside their boundary will not come under the legislation relating to party walls, and access is negotiable.