The only way these plants could have continued to run would have been with extensive maintenance - they were already running under a special permission allowing them to forgo scheduled maintenance. This maintenance could not have been put off any longer and would have meant the shutdown of the plants for an extended period as well as high costs that nobody (including the plant operators) was willing to pay. In effect, just continueing to run the plants as they were would have invited disaster by gross negligence. Another factor is the human factor: since the end of nuclear power generation has been a long time coming, a lot of the specialists at the various plants have changed their plans accordingly and moved to other industries or even countries to pursue new carreer opportunities, so that the knowhow and manpower to operate these plants simply does not exist anymore.
The real failure is that the existing alternatives have not been allowed to grow as needed. Previous governments have not just cut subsidiaries for power sources like wind, they have made it near impossible to install new plants with idiotic, over the top regulations and laws.
If you look to the UK, just as an example, not to pick on anyone in particular, there are a lot of individuals and families who still are unbelievably wealthy because their ancestors amassed incredible wealth either from slave trade or from endeavours relying on massive slave labour in the carribians. That money is still here, and it still allows the ancestors of slavers to live like little kings.
One prominent people this applies to is the new foreign secretary, David Cameron.
If you want to learn more, there is an article on the topic, and a public database of estates who have profitted from slavery.