The big trouble with solar power is, that it is not a reliable always on power source. Much of the power comes in a relatively short time around noon. So without extra buffering the grind can only use a limited amount (e.g. 5-10%) of PV. This can be better in sunny places than in foggy England, but this still is a major problem. Germany (not much more sun than England) already is close to the point where more installed PV is not really helping much, as on sunny days all coal / gas might go off line. So additional PV would have to be turned off for increasing times and thus get less useful output. Things are a little better with wind-power, but the problem is similar.
The part that is really missing is storage at an competitive price. It's only the first about 25 % renewable that are easy, as this can work without much extra storage.
England has very little fog. Where did that idea come from? The tails of pre-1960s London, with its killer smogs? Those are a thing of the past.
What really limits UK solar output is its northern location (obviously) and the large about of dense cloud that much of the country experiences for much of the year. Fluffy white clouds don't produce very heavy shadowing on the ground. However, for much of the time in the UK you can watch endlessly flowing shadow patterns sweep across the ground because of the dense clouds. In many places you can also hear endless creaking from houses as thing like plastic guttering heat and cool as each cloud passes.
As for storage, you are spot on. Look at any objective breakdown of what a country would need to do to achieve a high level of renewable energy, such as "Without the Hot Air". The potential methods of achieving a consistent flow of energy at the right time dominate the arguments made. Right now renewable energy schemes aren't even trying to hook in to traditional energy storage methods that many people already possess, such as well insulated hot water tanks. Sometimes the best use of spare PV energy would be to feed it to the grid. Sometimes the grid can't make good use of it, and it would be better to do something like heat water locally. Nothing currently manages this kind of dynamic resource allocation, so it just doesn't happen.