The default position when a country's electricity use drops 20% is to be concerned. If they do the same thing 4 more times they will have returned to the stone age.
If you look at trends, the main driver is the fall in industrial use, which has been consistent since the '70s. This country has effectively abandoned industry with Thatcher, and, unlike others, it has never looked back. British industry is in (un)managed decline, the economy is now entirely driven by services and finance.
Domestic trends are flat or falling softly, driven by those efficiency measures I mentioned. The UK used to have very cheap electricity coming from nuclear reactors that are slowly being decommissioned, which (combined with a typically-botched privatisation of the sector) has driven up domestic prices very significantly, pushing people towards alternatives. For example, there used to be a lot of electric heaters in British homes, which are now invariably replaced with gas-powered ones. That has not meant a significant fall in living standards.
There are many issues with the UK system, particularly a wealth distribution heavily skewed towards one or two metropolitan areas (the centres of services and finance), but falling energy use is not really one of them.
The UK temporarily outlawed older-generation lightbulbs, as well as putting in place a number of measures to reduce energy use. Even Conservatives, historically the party of industry, are now heavily committed towards energy-efficiency measures of all sorts (sometimes excessively so, like the push for those terrible heat pumps).
A decline in energy consumption is a good thing and is absolutely not impacting standards of living in any way in UK society. The reasons for discontent are many, for sure, but not related to energy use in any way. The main issue really is wage stagnation (and hence, availability of time) for the working classes.