To cut a dash means to have a striking attractive and elegant appearance, which is what he would like to have among the upper class in London.
Consider the staetement "Lady Cameron, he began, I am a simple country lord who doesn't want to spend the season in London and look like a dashing and fashionable gentleman among the upper class. ". Based on this statement, is "Lady cameron, he began, i am a simple country lord without any aspirations to spend the season in london and cut a dash among the ton." a true statement? Yes/no/unknown