Go here:
https://www.freebmd.org.uk/cgi/search.pl
Put a tick in the 'Deaths' box.
Enter your father's surname and first name.
Use the 'Date range' field to input the date of your father's death as accurately as you know it. Note that 'Mar' doesn't actually mean March. It means the first quarter of the year. (i.e. January to March). Similarly 'Jun' means April to June, 'Sep' means July to September and 'Dec' means October to December.
Leave everything else in the left-hand panel blank.
If you know the district where your father's death was probably registered in the England or Wales, select it under 'Districts' OR if you only know the county, select the appropriate county. (You only need to complete ONE of those fields). If it could have been anywhere in England or Wales, select either 'All districts' or 'All counties'.
Click 'Find' (at the bottom left of the page).
If there's a death certificate recorded, you should see a page like this one:
https://ibb.co/xCKn64V
Note that there's only one entry on that page. If your search criteria were imprecise, you might see lots of entries. If nothing is found, you simply get a page like that one with no entries on it.
The page in my illustration shows that Michael Dennis Peaty died between January and March 1973 (because, as above, 'Mar' doesn't actually stand for March). He was born on the 30th October 1952, with the relevant entry in the summary register being in volume 4B of the one for 'Mar' 1973 for Ipswich, on page number 3114.
If you can find similar information listed for your father's death, it shows that a death certificate definitely exists and provides you with the 'GRO reference' to order a copy of it from my link above.