There is no issue with renting, though you will need to get permission from your landlord.
As you are in England, you will need to register with Ofsted. To do that, contact your local Children's Information Service. You can find their contact details using ChildcareLink .
Ask them about Registering as a Childminder, they will be able to give you further information, a registration pack and details about a training course.
As both your children are over 8, it will not affect the number of children under 8 for whom you can care. The maximum allowed is 6 under 8's, though it does depend on house size.
You need to complete the Registration form and send it to Ofsted. There is also a form for anyone over the age of 16, plus a health form. Note: Your doctor may charge you for completing the health form, they can sometimes charge quite a high amount.
Paperwork can take 3 months, sometimes more, sometimes less. Ofsted will send an inspector out to your home to check it's suitability.
Get yourself a copy of the
Guide to Registration for Childminders
Childminding Standards
Guidance to the National Standards
Revisions to the Guidance
Hope that helps.