Just fallen foul of this.
Last May I was hit be a motorbike. I contacted my insurance company who provided a hire car. The third party admitted full liability and all my insurance companies costs were met. I got a letter stating this to be the case and that my no Claims was not affected.
Fast forward to last December and I renew my daughters policy with me as a named driver (this usually reduces her premium). On the application I stated that I had no claims in the last five years, thinking that my no fault claim would not count.
It transpired that her insurance company did a check and it revealed my fully settled no fault claim. Long story short, they demanded another £124 on her policy to have me on as a named driver. They stated this was because of my claim.
My partner renewed her policy this month with me as a named driver and also a check price without me. Declaring my claim increased her policy by £80.
TL;DR yes, a no fault claim will increase your own insurance costs going forward. I would suggest if you have a no fault accident, do not even contact your own insurer and let the third parties insurance deal with it.
Its an absolute scandal. It has further cemented my utter hatred of insurance company thieves. Along with ripping old people off over renewal fee’s etc etc. As far as I am concerned they are no better than people who burgle you.