From a British perspective:
Biggest US Sport in the UK is by far the NFL. This is down to TV coverage and the amount of effort the NFL puts in to the fanbase over here, with the games at Wembley stadium.
Also, Sky Sports is the promised land for sport, they know how to promote things well to make the sports they have the rights to the most important in the country. That's where the NFL is, and Sky push it like hell.
By contrast, the NHL is on Premier Sports - a niche channel that you have to pay £12.99 a month to watch. It shows a fair amount of hockey - Swedish League, EIHL, Champions Hockey League and Internationals. It's the only place you'll see hockey on TV in the UK. Aside from hockey, the channel has weird Irish sports and motor sports, with the odd football (soccer) game. It's not a channel that you'll pick up new viewers from - people are paying to see something that they're already a fan of.
Professional wrestling may even be bigger in the UK than hockey. I'm not sure about basketball. Obviously it's something that's played in schools across the country, and we have a league - but the attendances don't match those of the EIHL. The NBA is on BT Sports - which is a much better channel than Premier Sports - but I don't know numbers for how much more popular it is. The NBA did sell out the O2 recently.
As I'm sure many of you are aware, the NHL ran two games at the O2 in 2008, which sold out with almost 18,000 tickets. And, in our own league, the Manchester Storm set a record attendance of over 17,000 in 1997. It wasn't a one off, and they had a few successful seasons attendance wise - but that didn't last long, and the team folded in 2002. (Recently reborn - but that's another, complicated, story)
London is a crowded sports market, and very expensive for people in other areas of the UK to travel to/get hotels at for games. But it also has a large and culturally diverse population. And a population that's used to paying high prices. A quality hockey team playing in the KHL may encourage some ex-pats from 'hockey countries' to go to the games, who may not be interested in the EIHL due to the standard.
It's very interesting - and I hope it works out. It could be the catalyst that allows this country to grow as a hockey market. I think it rests on the arena chosen, the quality of the team on the ice and perhaps most importantly, media coverage. Getting the media in this country to care about hockey is hard. If London were getting an NHL team it would probably be huge - the KHL will not be as huge, but hopefully it stirs up some excitement.