The new process means that relatives will no longer have to wait for complex legal issues to be resolved before they can receive a payout.
Phil Stafford, head of underwriting standards, philosophy and claims, said: "Payment of death claims can often be delayed by the time taken to obtain the appropriate grant of representation, known as confirmation in Scotland, which enables the personal representatives to administer the deceased's estate.
"This delay can arise where an own life plan has not been assigned or written in trust. In complex cases the process can take many months or even years."
Stafford said the last thing anyone dealing with bereavement needs is the added pressure of money worries.
Life cover claims up to the amount of £100,000 will be paid out if there is a will and there are no suspicious circumstances.
For cases without a will Bright Grey and Scottish Provident will pay out up to £25,000. In all cases claimants will need to complete an indemnity form. This will allow the proceeds to be paid quickly without the need to wait for a grant of probate.
Stafford added: "We would also urge people to write their life policies in trust. With less than 10% of protection policies being written in trust many families needlessly experience the difficulties such as problems with probate, legacy disputes and unintended gifts to the tax man."
