Personally, I am not sure that comparing now with May (or whenever) is that valid so far as positive tests are concerned - not only are there a lot more tests, they are testing in areas that are thought to be hotbeds of infection. So no surprise that the numbers are going up.
What is more concerning is how quickly the numbers are rising now, under the new testing conditions. From the BBC Website - 'The government's science advisers say the number is now doubling every week. If those trends continue then infections could go from the estimated 6,000-a-day to more than 100,000 by mid-October.'
That's a frightening number, and of course there is no reason why it would stop at mid-October. In fact at doubling every day, by the end of October (say another 10 days) virtually everyone would be infected.
Once the numbers get that high, it would seem increasingly likely that that vulnerable people would find it incredibly difficult to avoid infection - and then the number of deaths would increase similarly.
I think many older people are still isolating as much as they can - for exactly the same reason that many young people aren't: the likely seriousness of the consequences should they be infected. So at the moment the death figures are low because of that self imposed isolation - once that becomes ineffective, we're screwed.