You need to read the small print on all policies - they're not all the same. Most insurers now provide a 14 day "cooling off" period during which you should satisfy yourself that you've got the cover you expected. If not, cancel within that period and get your money back.
It's been mentioned before, but as most potential MINI owners will be buying new, you need a policy that includes "new car replacement" for the first 12 months of ownership - or separate gap insurance. Of the companies mentioned on this site so far, it appears that Elephant does not include this cover in its policy. Elephant's wording can be read on-line and it also has a nasty looking "road rage" exclusion.
If any MINI2 member has a specific insurance problem and wants assistance resolving it, I'd be glad to try to help. If it can't be aired in public, send a private message.