If you are the sole owner or tenant you will continue to be liable for the whole of the payments.
If you and the person who has died were joint tenants or owners, you automatically become liable for the whole of the rent or mortgage.
If you are the spouse or civil partner of the owner or tenant, you will normally become liable for the rent or mortgage payments once their estate has been settled. However, you may also be liable in the meantime if you are their personal administrator. Either way, it is important to ensure that the rent or mortgage is being paid to avoid building up (or increasing) arrears. Contact an adviser or solicitor if you are unsure about anything.
If the property isn’t in your name, and you’re not the spouse or civil partner of the owner or tenant (eg. you are cohabiting) the situation is more complicated. You may not be legally responsible for paying the mortgage but will probably need to ensure it is paid in order to protect any legal interest you have in the property. You should get advice as soon as possible to find out where you stand.
Visit advice near you for your nearest advice surgery or contact a solicitor.