When people hear, "exponential growth", they confuse it for rapid growth. Exponential growth can be slow. In fact, that's what we're seeing in the UK now. An R0 of 1.1 is still exponential growth. It just means the case doubling time will be 3 weeks instead of 3 days. It seems pretty clear from the official figures the R0 is hovering above 1.
The lowest 7-day average daily rate of infection since lockdown was 545 cases on July 8th. It has been climbining steadily since then and is now 662. When it gets to a daily average of 1,090 cases, that will give the approximate doubling rate. As the number of cases rises, we would expect doubling to accelerate.
Seasonal attenuation means transmission is likely higher than is being recorded, because there will be a larger proportion of asymptomatic transmission, but let's use the official figures and assume the doubling rate is roughly 3 weeks with no acceleration.
July 8th - 545 cases per day (CPD)
July 29th - 1,090 CPD
August 19th - 2,180 CPD
September 9th - 4,360 CPD
September 30th - 8,720 CPD
October 21st - 17,440 CPD
and so on. Nothing has to change. The virus just needs to keep spreading at its currently seemingly low rate and we will see a second wave, with a large number of cases at the end of October. Add schools into the mix, and even if they only make a 20% contribution to the growth rate, we will see a signficant acceleration in infection. If seasonal attenuation is a factor with the SARS-CoV-2 virus, the numbers will be even worse.
There are those on MN who believe they can solve the pandemic through wishful thinking. If they succeed, I hope they'll use positive vibes to cure malaria next 
I'd rather put my faith in science and public health measures that are proven to work. Children and teachers need to wear masks in school, class sizes need to be reduced as much as possible, and people need to take whatever steps they can to reduce transmission by minimising social contact.