To be clear, not only were total deaths in England above (6.8%) the 5-year average in week ending 16th October, but they were also above the maximum number observed in that 5-year period.
The reason that this is not classed as statistically significant is that, if you observed 100 years of deaths instead of just this one, then you would expect to see at least 1 year where the number of deaths this week was the same as we have observed. That is very much not the same as saying this is normal or expected.
Also of note is that within the areas of the country that we know have the highest infection rates currently (North West, North East & Yorkshire, Midlands), not only were the total deaths above average but those rises were indeed statistically significant. To use the above explanation again, that means their numbers fall outside the range that you might expect to observe at least once in 100 years.
Edit - I mean in 100 ‘typical’ years, not years of pandemic or war, etc.