Is your rental contract a fixed term? If you have not given notice then why are new tenants coming round anyway. Landlord must give at least 24hours notice no matter what the terms are.
No they cannot, it is against the law, they cannot enter your home without permission from you and they legally have to give you at least 24 hour notice, they are especially breaking their part of the tenancy agreement by letting other people into your home when you have not handed in your notice, once a landlord gives you the keys to their home they cannot legally enter without your say so.