Moving email provider from BT to iCloud mail

As our family all have apple products we have decided we would move from our existing BT email accounts to iCloud mail accounts. WE are also switching broadband provider away from BT. We want to transfer all our emails and mail folders from our BT accounts to our new iCloud email accounts. I can't seem to find any instructions on how we can do that. Is it possible and if so how? Would welcome any advice!