In the interest of disclosure, I’m not Japanese. From what I know, it’s not really polite to talk about the Imperial Family. I tried asking a few people about the Emperor a few years ago and they gave me evasive answers. Eventually, someone was direct enough to tell me that most Japanese avoid discussing the issue in a casual way. That factor is probably what keeps the public from changing the Imperials into celebrities the way the Royals are treated in the UK.
This is in relation to the older generation, though. Younger people seem not to know much, or care to know much, about the Imperials. I doubt most of the people under 30 would even know more than the Emperor’s name. Some of them don’t even know that. Of course, that may be over-generalizing that last from a few airheaded girls I hit on in my first couple of years here.
Take a look at the fairly massive Wikipedia article for more information than you probably wanted to know about the Imperial Family, succession, and related issues like marriage outside the line of succession.
The difference in attitude between the reverence shown the Royals in the UK and the Imperial Family in Japan has a lot to do with time, I think. The Emperor was the Emperor up until 60 years ago. In contrast, it’s been a lot longer than a generation or two since the British monarchs were seriously in charge of governing.
Also, Westerners in general, and the British in particular, have a lot more casual attitude toward monarchs. The Magna Carta dates back to about 800 years ago. A similar idea of reciprocal rights and responsibilities was forced on the Japanese from the outside in very recent times; they never had anything similar in their history.
There are also still people around who were educated during the War years when the Emperor was held to be of divine birth and was the head of the official state religion. Their kids were probably raised with more of a sense of reverence toward the Imperial Family than subsequent generations who grew up in a time when the Emperor was nothing more than a figurehead. The only-just-post-War generation is the group that’s mostly in charge of the government now.
There are forms of address and formalities of language that you are supposed to use in speaking to or about the Emperor. I have no idea what they are, I just know that they exist. Most Japanese people don’t know the proper forms either, so I don’t feel too bad about that.