The government of 18th century britan was undemocratic because

Let's first learn what democratic means, ideally a democratic nation is ruled by all groups including the minorities in which the government keeps their noses out of most things.

At the time there was much prejudice against minorities most of who were Catholics. These minority groups were constantly discriminated and persecuted against in social and political lives.

Another reason is that the population was growing rapidly and without any sort of electoral reforms which allowed a more government intervention and actions to be allowed, thus making any small voices unheard. Which is the definition of a Republic system.