Insurance premiums spike mostly because repair costs have climbed, claims are up across the board, and insurers adjust their risk calculations yearly. Your personal driving record and claims history matter too, but even clean drivers see bumps. The thing is, insurers bank on people just paying without pushing back.
Calling them and asking for a breakdown of why your premium went up is step one. Sometimes there's genuinely nothing to negotiate, but other times they've bundled you into a higher risk category by mistake or there's room to discuss loyalty discounts, safety features on your car, or bundling home and auto. As that other answer mentioned, there's real leverage here if you're willing to use it.
Here's what most people miss: shop around before you call back. Get quotes from two or three competitors and keep them handy. Then ring your current insurer and tell them you've got better quotes elsewhere. A lot of the time they'll match or beat it to keep you, especially if you've been with them a while. If they won't budge, you actually switch - takes maybe 20 minutes to sort out. Don't just accept the renewal notice thinking you're stuck. They're counting on inertia.