Bypass masters and get PhD instead

[Alpha]

I think there is another factor at play here, regardless of whether you are applying to a US or a British program.  Many of these programs have competitive admissions.  There are a limited number of open slots.  This is common in PhD programs because each candidate must have a doctoral advisor, a committee, etc.  While the admissions criteria may not state explicitly that a Masters is required for admission to the Doctoral program, if you apply with just a Bachelors you may find yourself going head to head with a bunch of people who already have grad degrees.  In that case there may need to be something very special about you or your degree/university in order to win that competition and be awarded a slot.