Many of the features of the empire are regrettable. Slavery, which you didn't mention being one of the worst things, and a primary source of wealth for the colonialists.
The way in which indigenous cultures were treated was appalling, in Africa, Australasia and many other places, America of course being another example.
Also worth bearing in mind is that those who benefited from the empire were only an elite at the top of the social pile. Conditions in Britain for workers were very bad during the empire period,severe poverty was rampant,and the ill gotten gains of colonialism were appropriated by the ruling class. The same ruling class who were willing to sacrifice the lives of millions in the pointless imperial war of 1914-18.
That said, although I regret the empire, I don't feel shame, as it was previous generations who did all that.I might as well feel shame at just being human, given all the abuses humans have carried out globally over the entire course of history.On the other hand, I am certainly not proud of this country or it's blood soaked past. I'd like to see an end to the British establishment, but they have a way of hanging on. I suspect that during the next century we will see Britain reduced further to the status of a minor and insignificant player on the world stage.
Blackbill - are you from the UK? I suppose the differences in our perspectives if you are, may come from my being born and brought up in a former colony. The impact of what happened to the indigenous people here in NZ is still occurring here. Maori land disputes under the Treaty of Waitangi are still a very real and ongoing thing here. Maori are vastly over represented in crime stats and health stats due to an often very low socio economic status, not to mention what I hear my fellow Pakeha (fellow European New Zealanders) saying about them sometimes when they feel there are no Maori around. Here, we can't just say 'Oh well, it's done now, and was done for the best, and I personally didn't do anything wrong, so why don't they just get over it?'. For the country to move forward as a whole, changes need to be made, and rights need to be wronged. This is happening, but slowly, and changes in attitudes will take time.