Peachy
I am sorry to hear about your Dad which must have been unexpected
so life aint that peachy at present
Here is a useful link
https://www.gov.uk/after-a-death/organisations-you-need-to-contact-and-tell-us-once
also called do once and share
and this works amazingly quickly and efficiently
I would do it by writing as you have a few deadlines
If he was a form filler then his tax return should have been in 31 Jan 16 for the year ending 5 April 2015 - and there is another one for 5 April 2016 which is due yes 31 Jan 2017 but you just as well get on with it. Being dead is an allowable reason for a late return
The tax man will add the two together after the separate calculations and tell you if there is an overall rebate ( = offset ) . I had a fren who died 13 April so I was SURE that tax owed for that year was zero and well inside the personal allowance - and they said sorry he owed on the previous year...
keep written records and fill out the forms required