Quite so - that's why I referred to "voltage reductions and agreed turning off of big industrial loads". The Echo made the same point later in its piece, describing events in various surrounding areas, for example:
"There was no actual cut-off in the supply of electricity in the Birkenhead area to-day, and the Echo is officially informed that the necessary saving was effected by lowering the voltage and by the co-operation of industries."

In addition, I think you have taken those figures of 5 per cent etc. as reductions in voltage - which I did initially too. But when read carefully, it becomes clear that they are literal power reductions. Of course disconnecting a big single load is easier to include in the count of savings that way.

 
The more modest levels of "power cut" such as 5% do indeed almost certainly refer to voltage reductions.
Not certain about 15% though as that is an improbably large voltage reduction.

Voltages were not standardised in that era and varied from one district to another, there was still a fair bit of DC.

A 15% reduction would prevent proper operation of many appliances, especially under worst case conditions such as an already rather low voltage before the reduction.

Worst case might be a nominal 200 volt supply that was already down to  an actual 190 volts at  the intake, and down to 185 volts at the point of use. A further 15% reduction would result in only about 160 volts at the point of use.

A 200 volt lamp run at 160 volts will give a truly miserable light and tempt most consumers to use extra lamps or higher wattage bulbs, thereby increasing consumption.
A 200 volt heater run at 160 volts will be significantly less effective and prompt use of an extra heater if available.
Electric motors would be at risk of stalling and perhaps burning out.
Fluorescent lamps might fail to start.

 
I'm not sure there is a single date when the severe weather of 1947 started, even in a single place, let alone the whole country. It was already a cold winter with disruption to rail services before Christmas. So when did "bad" cross the line to become "severe", or does it need to be "very severe"? And who's judging?

For example, on 7th January the Liverpool Echo was reporting nationwide power cuts after three days of bad weather:
"Starting with a 5 per cent. reduction at 8 a.m., the cuts were increased in stages to 15 per cent., but after a short time 1.5 per cent. cut continued until noon.  Liverpool was more fortunate than some districts where a complete "cut-out" was made, and many breakfasts were cold."

Note the linguistic point that at this date "power cut" means a power reduction, achieved by voltage reductions and agreed turning off of big industrial loads. "Complete cut-out" or "black-out" were used for what we would call a power cut. Plus of course the electricity supply was still recovering from the war, so power cuts (or black-outs) were still quite common in a "normal" winter.

The later flooding has a much clearer start date, at least for a given place - 14th March in Reading. Talking of which (and climate change) I was at one of the Environment Agency's meet-the-people events about the Reading/Caversham flood barrier and came across this guy who was convinced there would never be another Thames flood. His "reasoning" was that we would not get much snow, due to warming, and the last big flood was due (only in part, actually) to snow melt. I got drawn into trying to put him right, which was of course pointless, and just led to him thinking I was EA staff (they were under strict instructions to avoid anything resembling an argument, even at the cost of not putting the arguments across).

One point I was trying to make was that the biggest known flood (based on flow measurements) was in 1894, and was in early November. No snow involved - just three days of heavy rain in the Thames catchment - and with negligible benefit of global warming, too. But there is still a memory of 1947 (partly inside living people), and none of 1894 (and surprisingly few photos).

 
Since 1963, the Central England Temperature series has recorded a mean negative value for a month only three times: January 1979, February 1986, and December 2010.

My grandad was a Midland Red bus driver in 1948 and he used to tell stories of how he helped reach villages that had been cut off for 3-4 weeks, with a snow plough fitted on the front of the bus.

 

We certainly don't seem to, though 1963, 1981 and (to an extent) 2010 were no too far away.  As every year passes the chances reduce, though it's still not impossible.  With twelve years since any significant falls, you can bet the railways will grind to a halt in the south when the next one does arrive.

 
The shortage of electricity was slightly alleviated by the use of moored diesel electric submarines to supply electricity to ports and coastal towns. Only in general applicable to places that used DC supply.

The submarine crews hated this as the considerable air flow needed by the engines resulted in a freezing cold draught throughout the vessel, for days on end.

Known as operation blackcurrant.

 
"We don't have winters like that any more ..."

From https://en.wikipedia.org/wiki/Winter_of_1946-47_in_the_United_Kingdom


See also
https://blog.metoffice.gov.uk/2017/01/26/winter-1947-brought-a-freeze-to-post-war-britain/
https://www.metoffice.gov.uk/weather/learn-about/weather/case-studies/severe-winters