Correct, you will need to apply for a BRP before citizenship. Shame you didn't stop by before hand! If you had done citizenship first, THEN changed your passport you could have saved a chunk of change.
It used to be that you could apply for citizenship in whatever name you wanted, but they changed it about a year or so ago requiring that citizenship be in the name of your current passport and visa. So you'll need those to match to apply.
And I hate to break it to you, but citizenship is just under £1,300, not £800.