It is not possible to perform Last Rites for a dead or unconscious person. Last Rites is the final Communion given to a dying person to cleans their soul so they will be allowed to enter Heaven when they die.
The deceased, or the comatose, cannot eat, drink, or confess.
The entire series is one long historical inaccuracy.
There are far too many healthy grown men around for the 50s. 6% of the country's male population (aged 15 to about 60) was killed, and thousands more were injured, so a village as small as Kembleford would have been hit harder than larger towns and cities.
Also rationing didn't end until 1954.
So in the time the series is set, there were no tea parties, dinner parties, or fetes, "make do and mend" was very much still in effect, people were still as self sufficient as possible, and there was no cloth or money for extravagant wardrobes; especially not with the bright colours and patterns worn by the cast.