I've found that, during this second wave, judging whether the infections are growing rapidly, gradually or beginning to plateau has been much, much harder than the first wave. During March/early April, the rate of growth was so rapid, it was obvious when it was growing, slowing, flattening and then, finally, about to fall.
This time around, in the 104 days since infections began rising again (starting on 8th July, four days after the government lifted most of the lockdown restrictions), there have only been seven days where the daily rise in the 7-day average was more than 10%, and four of those occasions are directly attributable to the 16,000 cases which were missed over the course of a week and then added to two consecutive days.
Therefore, I don't think this wave has, at any point, been characterised by exponential growth. It has, however, been characterised by periods of gradual, steady growth, followed by periods of lower growth (and even some decline), followed again by gradual, steady growth. For this reason, I think it's too early to say whether we've peaked or not yet.
Just to expand on the explanation above, when the 16,000 missing cases were added to the figures for 3rd and 4th October, this had the effect of artificially inflating the 7-day average until 11th October. As soon as these days dropped out of the calculation, the 7-day average immediately fell by 9.1% (making this week's starting point look lower than the previous week's), since which time it has increased by between 1-5% each day.
As explained above, that is absolutely characteristic of the sort of growth we have experienced throughout this second wave. It's certainly possible that the rate of growth is slowing (and the most recent data for cases by specimen date suggest that it might be), but I would want to see a few more days' data yet before calling it.