No personal experience with having a bike stolen but I work in insurance and I'm training to be a lawyer so....
First of all check your policy regarding theft and how long the bike has to be unrecovered for before they will pay. Also check if there's any requirement for where the bike is kept overnight. If they want to be difficult they could argue that it should have been at home in your garage at night (if you have a garage and said it will always be in there at night).
Bear in mind that insurance companies are heavily regulated by the Financial Services Authority and have strict guidlines to adhere to (though many do not until prodded by someone with knowledge). They cannot unreasonably delay a claim without giving you a reason (and that reason cannot be spurious). If they're going to deny a claim they have to tell you promply and tell you why.
If you don't get the result you want you have to file a complaint with them. If they do not resolve to your satisfaction then complain to the Financial Services Ombudsmen. The very threat of this will often prompt an insurer to pay just becasue of the costs and bad image it promotes. If I was your mate I would have gone down this route a long time ago!
When you're talking to them mention the FSA handbook ICOBS 8 and if they have any sense (they might) they will pull their finger out:
http://fsahandbook.info/FSA/html/handbook/ICOBS/8/1