I have to say living in Leicester, I've never seen any of this 'social or ethnic tension' you talk about. There are, like any other city rough areas, but as students we never go anywhere near them, I'll put it in context, the area where I live is 10 mins walk from campus and on numerous occasions i've absent mindely left my key in my lock all night, nothing has happened. The social makeup of Leicester and Southampton students (or indeed any other redbrick) will be almost identical, and we don't really have too much contact with the locals tbh.
Its funny, before I visited Leicester, your description was pretty much my perception of it, but when I got here I found that almost none of it is actually accurate, at least in my experience.
That said - go to the university where you feel you would be most comfortable, ignore league tables and crap like that if a uni has a decent historical reputation as both Leicester and Southampton do, then you will be just as well off in terms of graduation prospects at one then the other.