Clearest figures I can find on respiratory illnesses v. flu are in the ONS weekly deaths data release. Since the start of November, an average of about 950 deaths weekly in England/Wales were attributed to respiratory diseases including flu and pneumonia; in the same period, 2,600 deaths weekly mentioned Covid-19 on the death certificate.
I should make clear that this is not quite a like-for-like comparison, among other things because both Covid and another respiratory illness could appear on the same death certificate, and so some people are likely to have counted to both totals above. But it's not difficult to see reflected in the data that, if Covid is allowed to spread (ie, if we see more positive Covid cases), then it leads to a rapid increase in the death rate shortly afterwards consistent with the idea that Covid-19 is fatal in a larger percentage of cases than is flu.