You don't have to own your own home to adopt a child. As long as you have the space (i.e. one spare room per child) and are not at risk of eviction, then renting will not preclude you from adopting.

As part of the assessment process your agency will most likely ask for references from your landlord to ensure that you are able to provide a secure and stable home, along with evidence that there is a reasonable tenancy on the property that you live in and that you have the means to access another property should the tenancy end.