Finland needs ~15 GW in cold winter evenings, and that's for a population 12x smaller than in the UK. I've seen numbers like 720 GW for the US peak demand, which is comparable to Finland.
The future will mean energy abundance during most of the year. An S-curve of cost decline and deployments means even 1TW could be a low estimate
Northern Africa is having a massive solar boon right now, with lines delivering across Europe.
https://xlinks.co/morocco-uk-power-project/
It blew my mind you can transmit power for 3000km/2000mi with only about 10% loss using high voltage DC power lines.
The smart money would be buying ammonia synthesis equipment to site in Africa, instead, to sell to Finland and wherever the wind has let up.
That 1TW is nameplate peak production. New solar installed in good sites has a budgeted capacity factor of 0.2, declining gradually as the panels and associated equipment age.
If loads (demand, storage) are not well matched to solar production, realised capacity factor could well be 25% lower.
We'll want more of everything as the developing world develops and wants stuff and as demand for air conditioning grows. Vaclav Smil estimated world primary energy supply as 10 TW continuous as at 2000. since then it has near doubled with China's sudden rise. We'll probably want 50% - 100% more by 2050 as India and Nigeria develop.
0.2 TW continuous per year (the optimistic figure) growth in solar is not fast enough, IMHO.
1. Energy in Nature and Society, Smil V.
Of course solar is not the only renewable benefitting from production learning curve.
Taking into account engineering considerations like reliability, operating life, material properties in various environments, product quality, safety, known materials performance, operating life, and especially costs, capital and operating -- taking all those into account, the best uses for any electrolysed* hydrogen, made as a use of otherwise unused electricity, seem to be making fertilizer and hydrocarbons.
The latter are very energy dense, super cheap, and safe to store for long periods and to transport long distances to where the stored energy is needed.
Those two products are best made at isolated large scale dedicated plants operating continuous processes. It's not clear to me that hydrogen as hydrogen has any role as an energy storage or transport medium, nor is it clear that PV alone is a good fit as the energy source for the likely uses.
* I'm guessing by hydrolysis you meant electrolysis to produce hydrogen? "Hydrolysis" means "chemical reaction occurring with the addition of water", e.g sucrose -> glucose and fructose.
Handling of LNG and LH2 are not very different, a matter of volume and temperature. Where we handle millions of tons of LNG today, we can handle LH2 in its place with some adjustment. The people doing the adjustment will see a big job, but we won't notice.