Will being a named driver on another policy affect my no claims in the event of an accident?

No, you will not lose your no claims bonus if your wife has an accident because these are two separate policies. On her car insurance policy, you're just a named driver and although her claiming on the policy does not affect your other policy, if you happen to claim on her insurance policy where you're the additional driver, she will however lose her no claims.

If that doesn't make sense, let me know and I'll try to rephrase it.