In the U.S. what you want is normally called an inland marine policy, which covers actual replacement cost in the event of loss/damage. Couple that with liability in case you hit someone with that giant lightbox and you're good to go for a pro. Costs are usually around $2.00 - $4.00 per $1,000 per year. Companies that specialize in photographer's insurance are effectively giving you this. I'd imagine they have something similar in Europe. Best bet would be to call your current insurance company and see what they offer, and then shop around for other rates based on what they tell you.
Personal articles policies are fine if you're a hobbyist. If you make a single dime off your services, though, you'd better get it converted, because they'll deny your claim in a heartbeat if they find out. If you're planning on making money, you're already depreciating/writing off your equipment anyway, so get a business policy and write that off, too.