The insurer has demanded the change, in its response to a government review of inheritance tax.
This is because cohabiting couples do not benefit from a variety of measures that are enjoyed by those who are married or in civil partnerships.
This includes passing their estate to one another tax free on death and transferring any unused part of their inheritance tax nil rate band, which is currently worth £325,000, to one another on death.
Unlike married couples and those in civil partnerships, cohabiting couples also cannot transfer any unused portion of the recently introduced residential nil rate band (RNRB) to one another on death.
Helen Morrissey, personal finance specialist at Royal London, said: "Cohabiting couples can remain together long term, raise children together and share assets.
"Many cohabiting couples believe that after a certain amount of time cohabitees achieve some kind of ‘common law marriage’ status whereby they attain a similar level of rights to those who are married or in civil partnerships.
"However, this is not the case and a surviving partner can find themselves with a sizeable IHT bill when their partner dies. The time has come to bring these rules into the 21st century and recognise that not everyone wishes to marry."
Responding to a call for evidence from the Office of Tax Simplification for a review into inheritance tax, the insurer stated that the number of cohabiting couples had grown with an estimated 3.2 million cohabiting couples in the UK in 2016. This is up from approximately 1.5 million in 1996.
Royal London believe there would need to be safeguards in place to prevent fraud.
Couples would need to present evidence that they had lived together for a certain amount of time - for instance three years – before qualifying for the benefit.
In its response Royal London also called for the level of gifting allowances to be raised as well as a review of tax charges when a life insurance policy has been paid into trust.
The Office of Tax Simplification expects to publish its report in Autumn 2018.