Back in 1972, my father died suddenly on a Sunday, the church service in our little village church was the Wednesday, three days later, followed by cremation after.
Nowadays there is often a wait for the crematorium, about three weeks seems the norm, but of course it could be choice that the bereaved make to allow for folk to make plans.
Burials are probably ok if in a municipal cemetery that is cared for, grass cut regularly etc. My maternal family are in a lovely quiet little village churchyard, but am very aware when I have died, no one will come and put the occasional flowers on, or tidy it up. Their graves will end up like so many others, overgrown, untended, illegible headstones, forgotten, unloved.