Managing personal Outlook.com account settings, security, and privacy
Thank you for your response,
It is "only an alias", but it was still concerning that this was still working despite a password change as if someone gained access to my gmail account they would be able to send mail as my hotmail account and I would have no way of revoking this permission.
I am aware that I can remove the alias from my gmail account.
In this case it was fine as I had access to both accounts, but I have reason to believe that one of my other old gmail accounts may have been compromised and I cannot access it as I don't have access to my old phone number. I couldn't remember if I had set this alias up there also and had no way of knowing if emails are being sent as me.
For anyone else interested - I have found a way to revoke this by scrolling back in my outlook emails to 2011 and finding the email that was used to verify that I owned the email address. There was a link in the confirmation email to revoke the permissions.