My son's car insurance quotes are cheaper by adding me (mother), does this affect his no claims or my car insurance?

You probably have years of driving experience and a substantial amount of no claims discount (NCD) along with the fact that you're a woman. Woman drivers are considered as safer drivers and all these factors contribute to cheaper premiums than if your son took the insurance by himself.

Since your son is the main driver/policyholder, he will be getting no claims bonus if he doesn't make any claims whilst on the insurance policy. However if you happen to have an accident as the additional driver, he would lose his no claims discount. Named drivers do not really earn NCB but if they make a claim, it affects the no claims of the policyholder.

As far as you are concerned, being a named driver on your son's car insurance should not affect your own car insurance. However if you do get involved in an accident, you will have to declare it to your current and future insurers and this will result in higher premiums for you afterwards.