That difference seems to arise because the report you cite uses a broad definition of influenza deaths. Page 2 says they're counting patients who "have influenza as a contributing or underlying cause of death, plus patients who received specialist care with an influenza diagnosis who subsequently died within 30 days".

In any case, boosting the number to 685 still isn't enough so that covid is "double at most", and boosting it to 1100 isn't enough either.