If you have to claim on a life insurance policy, send the policy to the insurance company with the death certificate.
You will usually have to send the original certificate, not a photocopy – so keep copies and use recorded delivery if you are worried about the document going astray.
If the policy was written in trust to the person making the claim, the insurer ought to pay out reasonably quickly. If this is not the case, the insurer will not pay out until probate has been granted.

However, if the wait for probate is longer than two months, the insurer should add interest – calculated from the date of death to the eventual date of payment – to the amount insured.