I tried that for years, but despite being the only legal requirement, I was refused insurance quote unless I went for Fully Comp.pretty cheap if you just have "third party" only
At the time I was insuring for about 10/11k. I explained that I would have gladly replaced the bike with my own money if stolen – also, saving about 2k a year could have helped the "new bike fund", but they didn't budge.
Not sure about the legality of it all (I want the quote at least), but hey.