I am still proud to be English. By the way I am surprised at the amount of people on here, who say we must say British not English. Can you tell me why?
If we're referring to the British Empire or it's involvement in the transatlantic slave trade, then yes, you should say British. As has already been explained, just saying English ignores a lot of the people involved. What you call yourself doesn't change that. I call myself Midwestern, but in discussing American history, that's not really relevant most of the time.
Calling the transatlantic slave trade just 'the slave trade' may make sense from an American perspective discussing our own history, but if we're discussing shitty things some British people have done that involves slaves, bonded labour, indentured servitude, and similar, then only talking about the transatlantic slave trade would be ignoring a lot of it. If we say all Brits now need to take responsibility, we're also ignoring how much has changed in populations - not everyone here has or knows of their ancestors that were even part of the Empire, and - as already said - some were enslaved by members of it, or have both enslaved and owners in their bloodlines.
I personally don't have any strong feelings about what my ancestors I did not know did, though to my knowledge, none of them were part of the British Empire as the only European I know weren't British and immigrated to the US after the War of Independence, if only just. I assume, like most people, I am a mix of the enslaved and those that supported, if not benefitted directly from the institution. If anything, I feel more pity for my kin that went through the Korean War and WW1 - I'm sure it was a horrendous time, much as the relative who died in 1918 after months with the flu and all the kids who had to carry on without her. Pride? Guilt? I don't associate those emotions with history and I don't see how they help anyone.
Knowing the impact and horrors of the past and what is being done about the ills of today is important, but I don't think there is any benefit to this idea that we should teach some people that all their ancestors were either horrible bastards that should continuously be apologizing for or poor victims. Pretty much all of us are a mix of those and more.
A lot of people have come to the UK including some of my own ancestors so the UK can't be that bad and people want to emigrate to the USA
And plenty of people emigrate out of those countries, and between those countries. That doesn't really say much about whether a country is 'that bad', just how different people look at their options (and the involvement of either country in the recent affairs of other countries that has pushed people to leave has to be considered). I mean, I would say the Chinese government is 'that bad', but there are plenty of Americans and Brits who choose to live there for various reasons.