I think different countries have different 'social classes'. In some, the upper classes represent the elite of practically everything, whereas the lower classes are very much falling behind. In other countries, such as the well-developed Scandinavian ones, there are practically no working class. Almost everyone has an education, and there is no actual 'upper class' - there is a financial elite and a cultural elite, but they are not necessarily the same people. Which means that just because someone's well off, it doesn't mean they have good taste or a sense of culture (although they most likely have more than the complete opposite end).
I'm not British, but from my experience with England so far, I'd say I'd be more comfortable with someone from an upper middle background or so. It's a combination of things - similar lifestyle, interests, someone who's family would match mine etc. The English aristocracy seem like a strange little group to me, and I don't really feel the need to participate in that. In other countries such as France, I'd be comfortable dating the upper middle or upper class - to the French, the gap is mostly in culture and education.
I can add I would never reject someone solely based on what their parents earn or where they were born etc., if they are otherwise a good match. It just happens that you cannot date everybody, everybody's interested in saving their time and emotional energy with the opposite sex, and you don't go looking for someone you are unlikely to be a good fit with just to prove you're politically correct or tolerant. At least I wouldn't. I can support myself and would never expect a boyfriend to pay for me or be the one to fund a house, but I'd prefer someone to be able to take care of their share. I'll be able to pay a decent amount for an apartment, and obviously I'd love someone who could go in 50/50 with me.