Many hosting companies and large companies send out profiles for new email accounts and other iPhone settings. For email accounts which have been created via a profile you can’t just go in and delete the email account itself as it is controlled by the profile. You actually need to delete the profile.

To do this go into Settings > General > Profile

Select the profile

Select Delete Profile

Note: Sometimes this seems to work but parts of the profile are left in place until the phone is given a hard reboot.