Lockdown appears to have had an effect on 'cases' reported at the link you gave.

I note first of all that the site you link to appears to be using self-reported symptoms. I don't think that is likely to be reliable for a number of obvious reasons.

Take a look at cases from tests in the South East:

https://coronavirus.data.gov.uk/details/cases?areaType=region&areaName=South%20East

There's clearly a dip, perhaps due to lockdown.

However, there is no corresponding effect on deaths:

https://coronavirus.data.gov.uk/details/deaths?areaType=region&areaName=South%20East

We don't care about cases, whose main purpose appears to be for manipulation and control. Cases are bogus for a number of well-known reasons and so therefore also (to some extent) is a death resulting from a 'case'.

Finally: deaths in more northerly regions turned over well before the November lockdown could have been the cause. (Check it yourself.)

I would add also that the curve is for the country as a whole, and there will be geographic variation in time baked into it.

The first peak in early November could well have been dominated by cases in the North (which reached a peak then declined before lockdown could have had an effect) while the second rise looks to be dominated by the populous South East.

Thank you Fon,
your scientific observation and analysis is helpful. I do not have any objections to it your point that lockdowns work; they delay deaths. The only point I will make about this is if you look at India and other countries which don't have the executive to enforce or civil will to comply with lockdowns, and what happens to deaths where the disease is allowed to progress naturally with moderate and consistent social distancing. (India enforced a huge lockdown, strong and intense for 2 months until it became economically unfeasible).

But your main point is correct. they probably do delay deaths. My objection to lockdowns is the cost is too high in countries like the UK which do not have pandemic management infrastructure (ie sars countries).
COSTS
Mental health is made worse by the propaganda needed to scare people to comply. massive parts of population rather than the max 0.5% whose long lives will end sooner.
mental health cost of schools and jobs closing.
PHysical health costs of scaring people away from hospital
Health costs of the NHS's ability to prioritise Covid patients (this derives from the same propaganda and NHS religiosity).

I have not gone into the economic costs which will cause far more deaths than saved with the interventions.

All this is to delay the deaths by a year or more of people with COPD like issues. IT DOES NOT MAKE SENSE.

Sorry to break this: but lockdowns work to delay disease progress!

Conclusion, the national lockdown from 5 November appears to have caused an immediate fast slump in new cases starting on 5th Nov and continuing until lockdown was released . . .

I'm glad to inform (with some sadness) lockdown sceptics, that it is almost certain that in these circumstances the lockdown worked.

In terms of the dynamics of these virus curves we need to be looking at a point before any peaks to get to that "X" point - because that's the point when things fundamentally changed in the dynamics.

You are describing an effect known as Hysteresis
https://en.wikipedia.org/wiki/Hysteresis

You are right. I would have expected the lockdown on the 5th Nov to only effect the cases number until some days had passed, as you correctly point out,nature takes time to respond to changes in input.

I have since found that the ZOE app lags the PHE data by 3 days to a week. So the peak detected by ZOE on the 5th actually started to form earlier on e.g late Oct. This is shown by the flat section in the middle of the plot PHE below from 1st Nov to 16th Nov.Hence the activity to slow the virus (whatever it was) started as you say before the 5th. E.g. T3 in Liverpool, Manchester and all Wales hard lockdown in mid October perhaps with lockdown everywhere from 5th. I cannot be sure but I posit the tier system was working and lockdown caused an acceleration(steeper curve in ZOE data from around 22nd Nov). Very hard to be sure.

You are describing an effect known as Hysteresis
https://en.wikipedia.org/wiki/Hysteresis

No, the analogy I gave is not an example of hysteresis as that term is typically used in science.

The point I was trying to make is that when trying to understand a mathematical curve we can't just look at a single point like a local maximum or minimum. These are important, yes, but other things like the first and second derivatives are also necessary to properly understand things.

In terms of the mortality curve in the UK we can, for example, see the 2nd derivative going from positive to negative about a week after the 1st lockdown back in March. The "brakes" were on at that point - and the question we need to ask ourselves is why?

It's clear that this fundamental change in the dynamics could not be a direct result of the lockdown as there will be a 2 to 3 week lag between "cause" and "effect" in this curve. It might be that people's behaviour had sufficiently changed a couple of weeks prior to this inflection point at the end of March to drive this change in the dynamics of the curve. It might also be just a natural progression of an infectious new virus. It might be a combination of both. It's a complex multivariate problem and undoubtedly there are other factors influencing the mortality dynamics too. It seems clear to me that seasonality is a big factor also.

We can think of a simple analogy again. Suppose we had a whole bunch of balls randomly whizzing around in a box and colliding with one another. We have one red ball and all the others are blue. When a red ball collides with a blue ball it turns the blue ball red. You can see that if we have lots of balls then initially there is going to be a very rapid increase in red balls (probably exponential in the initial stages) - but this progression is going to slow as time progresses because the red balls start off with pretty much only blue balls to collide with, but later on they're going to collide with more and more of the red balls as the proportion of red balls increases.

I'd expect there to be an inflection point here too at some point - but it's not "caused" by anything as such. It would just be a natural progression of the dynamics as the proportion of blue/red collisions decreases over time.

If we decrease the mobility of the balls - which might be analogous to social distancing, or lockdown - then we're going to delay the timing of the inflection point. How much we have to change mobility in order to create a significant time shift is not an easy thing to work out, but it's not going to be a linear response, that's for sure.

It's like the birthday paradox - if you have 23 people in a room there is a 50% chance at least 2 of them will have the same birthday (assuming each birth date in a year is equally likely). It seems far too low a number, but you're looking at "collisions" between any pair - not just one particular date. In cryptography these types of events are actually called collisions and they're important for working out things like the security of hash functions, for example.

The upshot of all this musing is that simply pointing at a peak and trying to tie it to some earlier "cause" is not a trivial exercise at all.