I am a student with a bachelor degree in business( second up honor).

But I figure out my own interest is math. So I applied for a math master in local university and I am going to start it in this September. This is a taught program. I aim to use the time to take some important undergraduate courses. After that, I will take a two year research- based master to make a better preparation for phd application.

Here comes my question. I notices that some top applied math phd programs require a first honor undergraduate degree in math/ physics. So obviously, I can't fulfill it anyway no matter how many good grades I get in the master and how many research experience I get. Does it mean they won't accept a student who doesn't have a math bachelor but managed to learn all fundermental and advanced courses in math?

Does it mean if I want to enter some top programs in UK/US, I can only take another bachelor?

Thanks for your help!