Are you less likely to be admitted to a phd program with a masters?

Some phd programs like for their prospective students to be entering with a bachelors only…earning a masters and then a doctorate in that one program. I will graduate next may with a masters in english and then apply to other schools to work on my phd. do you think that will be a mark against me that i’m not entering with a bachelors? if that doesn’t make sense to you or you need more info, message me. thanks!