It is possible to change your main account email via User menu > Your settings: 

In the Your settings screen, select the Security tab on the left-side panel and click on Change email address.

NB!  When changing the Account holder email, make sure that the new user email has not been added as a secondary user under Settings > User Management.  The Admin status needs to be removed from the user before deletion, otherwise, the Delete button will be greyed out.

NB! In order to retain all your tickets in Linnworks Support Center, you need to login to the Support Center via at least once prior to the email change.