I dont like trying to do these calculations myself, but on this occasion I had a look at the underlying data and unless I also managed to make a mistake (quite possible!) the BBC might have fucked it up.
I'm thinking the numbers they have plotted are a better match to 7 day running totals, not 7 day averages. So they should either have changed the wording or divided their numbers by 7.
But maybe I am wrong.
One sanity check we can do is to look at the grand totals and rates per 100,000 for the entire pandemic so far. According to the UK dashboard data before todays delayed update has arrived, for England so far there have been just shy of 100,000 hospital admissions in the 85+ age group (99,788 to be precise). They also show this as a rate per 100,000, in this case the figure as of yesterdays data was 7095.2 per 100,000, so just over 7% of all 85+ year olds have been recorded in the covid hospital admissions/diagnoses figures so far in this pandemic. And at the start of this data being available in the first pandemic wave, it took a little over 1 month, till 25th April 2020, for the grand total of admissions in that age group to reach 1% of that ages population. It is reasonable to conclude that even during a period that includes a sharp massive peak, the total for this badly affected age group was not increasing at anything as high as 0.1% per day. So per week is far more plausible for this particular moment in this wave than per day.
And in terms of raw numbers, yesterdays published figure for that age group was 269 people. The total for that day and the 6 previous days combined was 1,327. I dont have the exact figures they use for number of people in the English population who are that age, but it seems to be in the 1.3-1.4 million sort of range, and I could in fact figure it out properly and quite trivially by using some of the earlier numbers I mentioned for totals so far in the entire pandemic. I dont really like posting the results of my maths, but in this case I think yeah, just over 1.4 million.