Bereavement leave
Currently there is no legal entitlement to bereavement leave (although parents and carers will be entitled to bereavement leave following the loss of a child under a new law coming into force in April 2020).
The dependency leave provisions in section 57A of the Employment Rights Act 1996 entitle you to take a “reasonable” amount of time off in consequence of the death of a dependant (which includes a parent).
While these do not specify how much time is reasonable, they are designed to deal with emergency situations, and time off is likely to be limited to that required for practical arrangements and to attend the funeral. The statutory time off is also unpaid.
Many employers offer longer, paid compassionate leave to cover situations such as the death of a loved one.
If you have nothing in writing, then it would be worth asking your line manager or HR department of the policy or, if no formal policy, what they have agreed in previous cases so that you can ask for consistent treatment.