While the OP refers to the British grid, the topic is far from limited to the UK. IMO, the issue is the direct result of the exact same factors - and these factors are purely political.
Full capacity? How can that be, in this age of energy-efficient appliances and declining manufacturing?
Very simple: Reduced capacity. Power plants being shut down, and resources being denied. From San Diego's nuclear plant to the mandated shut-down of coal plants, we're losing generating capacity.
Solar? Look at what happened in Nevada: There the PoCo caught grief for using 'too much' of the 'wrong' sort of renewable energy (geothermal). Yet, when they attempted to build a solar farm, the very same 'solar advocates' blocked the plan, speculating that putting acres of desert rock in the shade of solar panels MIGHT somehow cause harm to the environment.
Likewise, the Reno, Nv., area suffered for decades as the direct result of activists delaying the construction of a second power line into the area.
NO amount of technology can fix what is a political problem. Believe me, the PoCo's know how to make and deliver power; all we need do is get out of their way.
If you listen to fools, the mob rules.
