To answer the OP's question- my advice is that you know your own DC and that is your best guide. My DC lost two very close relatives in the space of a year and they didn't want to attend either funeral service (but came to the reception afterwards). I had no problem with this- they still grieved and understood that those people were dead.
I do take issue with much of what's been said on here regarding cultural differences though. Which is that English funerals are cold and the English are fearful of death, whereas the Irish are much better at dealing with death. My own experience tells a very different story.
My DGM was Irish but left to escape being locked up in a Magdalen laundry in the 1930s as she was pregnant and unmarried. She married my English DGF and they had 50 years together. Her funeral was the full Catholic mass which seemed to go on forever (she had been so indoctrinated that even though she had never set foot in a church since arriving in England she still wanted a Catholic burial). The Priest knew nothing about her or her life and the church was packed with people who thought it was a grand day out! Several of her siblings came and came back to the house afterwards. They drank and ate everything and anything and waxed lyrical about their childhood memories of my DGM. Funnily enough not one of them had been in contact with her for the 50 years she had lived in England!!
As for the "cold English funeral" of my DF twenty years ago- nobody wore black, we had no church service, but we stood in a beautiful woodland and played his beloved jazz whilst drinking Champagne and celebrating about his life. The small number of people who attended were his actual friends and close family who had known and loved him.
Furthermore I don't believe it's unhealthy to fear dying, particularly if you are not religious. For us there is no redemption or afterlife so it seems logical to want to have the best life on earth and part of that involves being afraid of how and when it will come to an end.
Also please no more of the cold hearted English trope. Some of us like to do our grieving in private. Doesn't mean our feelings are any less. And it has bugger all to do with 'What would the Queen do'.
Ok - rant over...