But, as there is more likelihood of a PCR test picking up a past infection rather than a live infection, trying to tie cases to deaths - determined solely by PCR - is not realistic.

...which is why you need symptoms for a PCR test...
The death trend also follows the spike in hospital admissions and a spike in ICU admissions.
So with appropriate lead times the death curve follows the (i) cases (ii) hospital admissions (iii) ICU admissions.

You agree that mass PCR testing is an unreliable means of determining cases and deaths. We don't know how variable the results are because we are not given details of how these tests are performed. You have frequently stated that yourself. Why do you trust anything that they produce, let alone anything derived from them?

For example, the chart for 16 day lag using ONS daily figures as posted above is:

It looks very nice around the peak 'cases' around 1st January - but what about earlier on in the year?

Now let's have a look at a more realistic 21 day lag:

Well, that's a bit better earlier on in the year, but not so good now.

Let's try, arbitrarily, a 24 day lag:

Well, that fits perfectly for September to October - but way out after that.

It seems we can play tunes on this lag - but it is a flute with more holes than we have fingers. It is therefore natural to look for some other explanation. Vaccinations among the elderly may be one - but I am open to other suggestions.
It does not however follow anything like the shape of the vaccination graph.
If it walks like a duck...

To say "It does not however follow anything like the shape of the vaccination graph" suggests that your eyes need testing. If you were to say that a link is not proven, I would agree. But the similarity in trends looks suspicious to me.

We may have a few ducks here. No curves match exactly. Above, I have shown that the cases/deaths ratio does not have any consistency. And last week, I demonstrated how the vaccination curve looks like it has a correlation. It could form part of the explanation for spikes in death that the OP requested, but more investigations would be needed.

But, as there is more likelihood of a PCR test picking up a past infection rather than a live infection, trying to tie cases to deaths - determined solely by PCR - is not realistic.

...which is why you need symptoms for a PCR test...

The death trend also follows the spike in hospital admissions and a spike in ICU admissions.

So with appropriate lead times the death curve follows the (i) cases (ii) hospital admissions (iii) ICU admissions.

It does not however follow anything like the shape of the vaccination graph.

If it walks like a duck...

Fall in the various curves is due to 2 major factors.

Lockdown pressures (reduce transmission) and vaccination pressures(increasing protection)

The former should should be largely uniform subtraction from R, the latter an increasing subtraction from R (increasing with number of vaccinated people)

Lockdown pressures (reduce transmission) and vaccination pressures(increasing protection)

Natural seasonality as all HCoVs exhibit is a likely factor.
The former should should be largely uniform subtraction from R, the latter an increasing subtraction from R (increasing with number of vaccinated people)

Nope.
The former, if it works will result in a less steep curve up and down. Also lessening change as time goes on and fatigue sets in (modelled by SAGE, shown IRL by Lancet post studies of lockdown 1).

Vaccination pressure is still too new - the only place you'll see that is in the hospital admissions by age.
You'd expect to see an odd shift to the ratio of younger people there (and the media being hysterical about how it affects younger people).

Lockdown pressures (reduce transmission) and vaccination pressures(increasing protection)

Natural seasonality as all HCoVs exhibit is a likely factor.
The former should should be largely uniform subtraction from R, the latter an increasing subtraction from R (increasing with number of vaccinated people)

Nope.
The former, if it works will result in a less steep curve up and down. Also lessening change as time goes on and fatigue sets in (modelled by SAGE, shown IRL by Lancet post studies of lockdown 1).

Vaccination pressure is still too new - the only place you'll see that is in the hospital admissions by age.
You'd expect to see an odd shift to the ratio of younger people there (and the media being hysterical about how it affects younger people).

Ah yes, seasonality is the general alternative theory to tell the story of how lockdowns do nothing. Just doesn't explain the excellent time alignment, nor the decline in disease in November.

I think you mean less steep curve up and steeper curve down (or actually any down at all). That is what a reduction in R achieves.
I think adherence to restrictions remains pretty strong, but nevertheless the decline in cases is waning. An explanation I heard is that there are population sections that don't or can't isolate (affordability, dense housing situation, work conditions or non-compliance).

Vaccination pressure is starting to show in figures now. Relative reduction in cases and admissions is greater in older age groups. There are about 10m people with vaccinations at least 21 days old, so this is to be expected.

If people who are vaccinated are testing +ve for covid, as a result of the vaccination, would that not mask the issue in your dataset? Have you seen the data that Mike Austin linked in his reply to my post? Those data show a strong link between increased death rates and increased vaccinations. What are your thoughts on Mike's analysis?

I worked for 25 years or so making correlations with loosely connected data sets; the secret is not to put too much fantasy into the correlation - and if you are using a lot of fantasy then just admit it. Also it's always best to keep the interpretation separate from the correlation, otherwise you will be biased and not recognise that you are fantasising.
Now it doesn't take a great deal of fantasy to see that the correlation shown in my previously presented graph of positive covid rate verses death rate doesn't really change at all (at least not up to the last data point). In fact I would go so far as to say that the correlation for Italy is excellent while that for the UK is perfect and therefore this correlation has, in my opinion, a lot of weight. So now the correlation needs to be interpreted to try and find out what the impact, good or bad, of the vaccine program has been up until now. The answer to this is relatively simple because: 1) The UK correlation does not change at all up to the last data point, meaning that at present the impact of the vaccine on these macro numbers has been negligible 2) The "control" data set from a country assumed to be behind the UK in its vaccine program (Italy) also shows no marked change in the correlation.
So QED: based on the positive covid and death rate data sets the vaccine program has had no impact on the death rate up until now. The possible impact of the vaccine on the positive rate itself (that is what has caused the presently steeply decreasing trend) is clearly a political issue, so I'll leave that to others.
I'll take the opportunity to present a few other countries from the excellent Johns Hopkins data set:

Israel.
As far as I am aware Israel is ahead of the UK in its vaccination program. The death rate data is now shifted by 11 days (software best selection). Now you could fantasise that the departure from the falling positive covid rate trend starting around 22nd January and stopping around 3rd February was caused by a bad effect of the vaccine while the continuing fall in the death rate over the same period was a good effect of the vaccine. But my opinion would be there are so many other reasons for this blip that there is too much fantasy involved in assigning any causal relationship; therefore my opinion would be that the net impact of the vaccine based on this data set has been negligible.

America.
Back to a 16 day shift and another excellent correlation. But wait a minute. what's that up-tick just at the end of the death rate data set? Surely this must be the effect of the vaccine killing people? Oops, sorry about that, I was letting my fantasy run away with me.

Russia.
This time an 11 day shift. Of the data sets so far presented this is the only one that departs from the correlation in what could possibly be conceived as a negative sense for any vaccine program as the death rate seems to remain noticeably flat while the positive covid rate falls. However, it can also be interpreted in a positive way if it is assumed that the death rate curve flattening, starting around 25th November, was due to the vaccine program. So it's a draw as far as concluding what effect Sputnik 5 has had (although detailed further analysis would be beneficial).