I think if we distil it down there are three areas which the government has a high level of control over which you could reasonably 'toughen' and have measurable and testable effects on the 'R' rate:
1. Schools, i.e. widespread closures similar to march
2. Shutter more 'non-essential' workplaces
3. Stop 'take out' services
Of these, none are particularly attractive but having read and reflected on that LSHTM pre-print, their case around school transmission did look pretty convincing (caveat not peer-reviewed and not my science area). Options 2 and 3 would be quite damaging economically and frankly, I can't see them making much difference. Most workplaces are reasonably covid-secure and operating at much reduced capacity. None of our purely office based staff have been in since March. I can't imagine the local Costa or Starbucks being a nexus of infection!
Then there are the petty and vindictive measures the government seems to like putting in place, like the bizarre rules on social contact and 'exercise', potential expansion of masking, curfews and so forth. I've woken up every day these last three weeks wondering what nonsense they'll come out with next. The other issue with these interventions, is there seems to be little handle on how much difference they actually make to the R value. Some are possibly counter-productive as some of you have pointed out but fall into 'seen to be doing something' category. I'd also say many of these are more difficult to actually enforce than any of the three options outlined above. I think, unfortunately for the government, a lot of people have clocked that the ability of the Police to enforce a lot of these measures is limited. The few Police officers we have to cover the three fairly large towns in my area spend most of their time whizzing up and down to domestics and RTA's.
Round my way, in a 'tier 4' area, you would not believe we are supposed to be in some kind of lockdown. Lots of people and cars milling around. Swapping notes with a few mates and colleagues, there seems to be a lot of people out and about through exasperation and boredom, which doesn't bode well.