There isn't a nation on the planet that doesn't have more than a few blots in its history. The UK is no different, but it really has nothing to apologize for at the same time. The Empire was just a product of its time, not the fulfilled desire of some evil collective national consciousness. As for slavery, that is something that more nations than Britain have to feel bad about. Haiti were French slaves, the US had slaves until 1865, Brazil had slaves after that, and the list could go on and on. It's just one of those injustices that we have to hope never happens again on such a large scale. This kind of makes me think of Monty Python's the Life of Brian. "Bloody Romans! What have they ever given us?" "Well, it's safe to walk the streets at night, public education, etc."
Same could be said of the British. They took some things wherever they went, but they also gave back quite a bit more. Be proud of who you are and your past. It made you who are you are today.