Will a crash that wasn't my fault affect my no-claims bonus?

Why it depends on whose policy is used

When you claim on your own policy, your insurer pays for your repair and then recovers its costs from the other driver's insurer.

Source: Competition and Consumer Protection Commission, "Making a car insurance claim": "your no claims bonus could be affected for a time and you may have to pay the excess on your policy"; "the excess should be refunded once your insurance company recovers their costs."

When you claim directly from the other driver's insurer, the claim never goes on your policy. There is no excess to pay and your no-claims bonus is not used for it.

Source: Competition and Consumer Protection Commission, "Making a car insurance claim": "You can make a claim directly from the other person's insurance company."

You still tell your own insurer

Telling your insurer about an accident is not the same as claiming. For most insurers it is a condition of the policy, so let them know when you get a chance.

Source: Competition and Consumer Protection Commission, "Making a car insurance claim": "Notify your insurer as soon as possible, even if you do not plan to claim."

What we can and cannot say

We can tell you that when we claim for you, we claim from the other driver's insurer, not from your policy. We cannot tell you what your own insurer will charge you at renewal. That is a matter for them, and they may ask you about any accident you have had.

Your own insurer or theirs, side by side.