It's [the daily case rate is doubling in] about two weeks. I'd describe that as "fast" personally.
As I pointed out, the 'even larger' graph you share again is for daily cases in England.
The full sentence from which you quoted said "Case rate (UK) is down in the 40s per 100,000 and its current increase is slow, doubling in about three weeks." Given that there's going to be a third wave cases are 'bound' to go up (but low hospitalisations).
In response to your last "it's doubling in a fortnight and here's the maths prof saying so" I said:
Professor Johnson shows doubling in 14 days . . . . in England. Add in the other parts of UK and you get the estimate I shared.
Having said all that, today's case (
reported) number is another thousand up. There's some late reporting after the BH w/e - all the figures before the w/e, by specimen date have been augmented (and I have drawn that amended data into the revised graph below). That supports that the UK cases are set to double in about two weeks (a daily average increase since 16 May of 4.7%). If that rate of increase persists, I think the 'no earlier than' 21 Jun date relaxation is in jeopardy, or at least SAGE will be clear (and probably vocal, in a way that they weren't quite in September). Irrespective of the best for the country in the round which rightly will be a political decision, they must robustly represent the science/health factors. Furthermore they can see that 'history' is being fashioned under their noses: let's hope their frankness doesn't play out to be a 'Cassandra' contribution.
Data cut-off 29 May (data as at 3 Jun), orange line = 7 day average