Tenant's inviting partners to live in without permission

We are finding that many tenants are signing tenancy agreement with just their names on it and then a few weeks later their partners moving in without any notice or request which is of course a break of the agreement however how can you prove it as a long term stay tenant and what good will it do issuing notice when you have to look for new tenants again and lose money doing so?

How to avoid this as we prefer and need to know who is residing for insurance and other purposes. Can you include a clause stating that if another person is consistently residing then there will be a rent increase to X amount? Is this legal? As what they are doing is also not legal.