I recently renewed the insurance on my other car and told them I was just about to put it on SORN. The advice from them was to leave the policy as if the car was on the road, although they could offer alternative “laid up” cover. The reason was that if I then wanted to put it back on the road (I will be doing so once I’ve completed some engine modifications) they would otherwise have to charge me admin costs and the policy might become more expensive.
However, I think the best advice is to check with your own insurance provider.
Make sure you inform DVLA a few days before the end of the month, ie not on the 1st if December or you will be charged for Dec. Apart from that it’s a breeze to do online, I’ve done it for the last two winters and no need to inform the insurance, do keep your policy going.
I’m on a limited mileage policy so the insurers assume that it will be in the garage more than it is out. I asked them about laying up over the winter - there is no reduction and they didn’t need to be told if the car is SORN’d.