You're right about the assumptions, sorry.
Well, I agree that people shouldn't be arrested for outbursts like that; the punishment largely comes from the stigma of being an asshole. As far as bullying and hate speech, those should be arrestable offenses, as they are, without a doubt, a large engine behind many suicides in minority communities.
I think moreover we should focus on education. If our school systems were more functional (I'm talking about the US here, but I'm pretty sure that England's school systems aren't without flaw), more could be done to challenge racist and bigoted beliefs. Additionally, community diversity quotas could be of aid. However, all of this assumes that the industrial-technological system as it stands will continue to progress; this is most likely a false assumption. Because a large-scale breakdown is imminent, small autonomous communities will develop quickly, and there will be no other option than to work together and think ourselves through our ethnocentric beliefs. Without the ability to work together, to accept one another, and to understand one another, there is no chance of survival in the post-coercion-based-hierarchy era. There will, without a doubt, be a long, painful transitional period where these bigoted ideologies are key drivers in a chaotic and seemingly eternally warring race. There will be blood. But only after we tackle these problems will the chaos end.
You have to look at the big picture. Solving problems like these symptomatically is ineffective. You can write laws all day long, make ad campaigns, but as long as we live in a society based on (largely ethnocentric) hierarchy and coercion, greed and consumption, there is literally no chance of hope as far as dissolving ethnic, sexual, and creed-based issues.