As a northerner, I can say that it is true that "bitter" and "beer" generally mean the same thing to most people there. In the corner of the north that I'm from, if you ask for a pint of beer in a pub it will be assumed you mean a pint of bitter.
And make no mistake, people
do know that bitters and lagers are both beers - so it's not done out of ignorance. My theory is that it's a throwback to the days before lager became popular - so bitter became synonymous with beer. Even though that's
technically incorrect, people still know the score.