I'm no expert but here's what I understand from struggling with this myself.
If it's a .com address I suggest you take control of it with the actual registrant (easily.com?), and handle the renewals etc yourselves. The ISP can tell you the details to enter as DNS servers etc, and do the email hosting for you. The account should be accessible to you, so you can see who is the registered owner, who is the Administrative Contact, Technical Contact etc. If you make sure you are the Admin and Tech Contact then you will be prompted to renew by easily.com. If the registrant won't facilitate this, I suggest transferring it to someone more helpful. Networksolutions.com are brilliant.
If it's a .co.uk then I think you have to let your ISP manage the account for you.