If you are on BTMail and not BTYahoo you need to change your password via MyBT.
You need to log onto you MyBT and go to My Profile which is on the left side of the page above the Hi what ever your name is.
Scroll down to "My Security Details" and edit the password. Follow the prompts. This will also change the password of you MyBT.
See this link for the help pages.
If you are still on BTYahoo mail, click on the cog icon in the top right hand corner of the webmail page and select 'Account info' password change option is top of the links.