You will not be transferred any time soon. The migration stopped in 2014 and there are no plans to re-start it and you can not ask to be transferred or rather you can ask but it won't happen.
You are not stuck with Yahoo but if you wish to use the BT email system you will have to use BTYahoo email.
If you want you can use any other email supplier such as gmail or a paid for service.
thanks - I am concerned that yahoo has been taken over and that another company will have my personal data - from what you say I am stuck with yahoo
Yahoo's parent company is Oath Inc.
Since they are dealing with a UK (EU) company - BT - then they have to legally abide by the GDPR.