Third party fire & theft will be cheaper than fully comp,
Some insurance companys will be cheaper if:
You fit DRL's (those white l.e.d light strips)
Dash camera (records driving )
GPS tracker (car can be tracked if stolen)
Actually, it can quite often work out cheaper to go Fully Comp!!
In my first year of car ownership, I saved about £50 going fully comp.
Adding a driver with plenty of NCB and no convictions SHOULD bring the price down...especially if a parent/guardian/family member/spouse.
Also worth fiddling with your job description - The Money Saving Expert website has a job comparison tool that shows you the lowest risk job title within similar titles.
Be careful with any modification - some insurers will just see £ signs rolling in their eyes at the mere mention of them!!
Black boxes and dash cams are separate devices. The black box schemes give you a small GPS tracker that records your location, speed (and can use these two to determine if you're speeding), style of driving (rapid acceleration or braking) and also the time you drive. Drive sensibly and you are rewarded - but these do not take into account the overall situation (like having to do an emergency stop because some kid runs out in front of you). Dash cams are primarily there to record what's happening outside of the vehicle. SOME insurers are offering a discount on approved cameras (Swift being one, and I THINK the Co-op). Some cameras are also fitted with GPS antenna to record location data. To see why dash cams are a bonus, have a look at the various dash cam threads.
Trackers can be useful, although I have heard of at least one person having their insurance go UP because they fitted one. The reason given was that the car was more likely to be recovered and in need of repair - so overall more expensive for the insurers (thieving gits...no better than car thieves really!!)
Decent alarm system should help though.
Forgive my long post, I hope you find some use from it