I think E-P is proposing a reduction, not a shut-off. The reduction would come from sharply higher prices, I presume.

I believe the UK's residential heat is mostly electrical.

My understanding, and what has been reported on TOD before, is that homes are the last to see their gas shut off in an emergency. This is due to the issue of pilot lights going out and the resulting explosions when the gas service is resumes.

Ideally, home heating consumption would be cut back by efficiency measures.  There is no simple way to discriminate between over-heating spaces vs. heating water or cooking.

So what does this mean, that "If electric power generation loses, everything else collapses."?

If the electric grid runs out of fuel or is overloaded, almost every central-heating system goes down in the blackout.  This turns one failure into two failures, plus serious impairment of commerce (can't handle refrigerated food without fridges, most businesses can't run without electronic cash registers), etc.  Short-term fuel shortages can be dealt with by shutting down business, but over the long term this brings down everything else with it.

We can cut back a lot more on space heat than we can on electricity.

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Pilot lights is not the only reason. Gas is usually cut off to the biggest users first because they result in the biggest cuts in demand in the shortest time, and putting them back on is quicker. Less manpower and less persuasion (by force?) of reluctant users is required to achieve it. Also for political reasons, more users equals more votes.

If a gas network loses supply in an unplanned way, demand will fall off as users stop using the supply, whether manually or automatically. Valves in the pipelines may shut automatically or maually. This then may result in pressures recovering/rising in parts of the network. If those automatic cut off systems are not present and pilot lights are out gas will escape and cause explosions. Air and water can also enter the pipes if gas pressure is low. Half the low pressure network in some UK cities is over 100 years old and leaks are everywhere, mostly small but many of them. Getting this air and water out of the system is a big job.

Before a gas network can be turned on again after a cut all user supplies have to be visited to make sure the meter supply valve is off. Once all users are off the gas supply has to to be checked to make sure pressures are OK and there is no air in the system. This will be done in small groups of users dependent on valve locations and network layout. Typically a few streets at a time will have this done. It may involve digging holes in the streets where valves are missing or rusty. The switch from coal gas to natural gas in the UK in the 1970's was a similar project. When thousands of users are affected this needs huge numbers of qualified staff, vehicles and materials. A city of millions could take months to switch on again. This happened in Austrailia, can't remember the city.

I expect that sometime after 2020 a person(s) in the UK will have to decide which city will get gas and which will not. Once a city/region loses supply it may stay off, becuse the logistics of switching gas on again can't be justified when supply may dissappear again soon. This will cause mass movements of people to places where there is still heat, and political stress.

In Austrailian water shortages there were similar priority issues. Farms got cut off first, and cities/homes got the water. This was a short term solution with immediate political benefits. Long term people can live without washing but not without food.

(I worked for 12 years in the UK nat gas industry)