Firstly, Matt (short for Mathfew) Hancock said in his interview with Julia Hartley-Brewer,The number of people in hospital has doubled every 8 days in the last few weeks
I presume he meant covid-19 cases. They were at a (7-day average) minimum of 780 on 3rd September and rose to 956 on 16th September. Come on Mathfew, must try harder!
Maybe he meant admissions? The lowest admissions (again, 7-day average) was on 22nd August at 93. On 16th September they were 204. So they have gone up a bit over twice in nearly 4 weeks. Come on Mathfew, must try harder!
So the number of admission is indeed going up - and the number of cases in hospital is going up. But there are no figures for discharges. I have come up with the following. Please let me know if it makes sense.

As you can see, it should be trivial to determine how many people leave hospital. If we subtract the deaths in hospital (I have approximated this), we should see a better representation of patient turnaround. The discharges would appear to track the admissions closely. Perhaps more less-severe cases are being admitted and then released in a short time - or am I speculating too far?
The point is, of course, that one should not quote only admissions without corresponding discharges otherwise there is a distorted impression of the situation. We would not want to do that, would we Mathfew?