The relevant statute provides that the landlord can enter to inspect the property so long as they give 48 hours advance notice and don't abuse the right. Your situation is a little unusual as your landlords have personal property in the basement.
However, there is a sub statute about giving notice of a landlord's breach of the covenant of quiet enjoyment, and asking a court for relief. I routinely advise people *not* to get into a battle of the rights with their landlord, because in the long run, the tenant will likely lose such a battle.Writing to them and pointing out that you value your privacy and you feel invaded when they announce they just want to look around (or maybe they think you are growing pot or raising hamsters) and tell them it makes you feel uncomfortable.
Perhaps they don't know. Hope this helps. Elizabeth Powell