The total storage reservoir surface area of the UK's existing 20-30GWh of pumped storage is approximately 6 square kilometres
Even if math is not your strong suit, you should probably do some math - it is fairly simple, btw - to do a sanity check on those numbers.
I am sure the water and land in the UK are much holier, but the largest such facility in the world generates 3GW, and takes up 5 million square meters - compare with your figures.
BTW, that facility was built in a remote area, in the 1980s, at a then cost of $1.6Bn.
I would conservatively estimate that such a facility, if it were to be built in the UK today, would cost you well over $10Bn, assuming that you can overcome the political pressure and environmental approvals.
Again, being able to think critical and not taking other peole's BS wholesale helps.
Bath County Pumped Storage Station?
It stores 45GWh of energy in the upper reservoir of 1 square kilometre, roughly 10 times more efficient per unit area of land than the existing UK pumped storage fleet. Perhaps I should revise the above estimate for the total area in the UK needed to store 4000GWh down by a factor of 10?
I'm not sure how you arrive at the 5 square kilometres, but even with that estimate that counts an area larger than both reservoirs its still a factor of 2 more land area efficient than the current UK fleet.
Read the papers I have linked, they look at the current costs of building storage and estimate a comparable 50,000 ML system to cost several billion dollars to build around 2 billion.
For comparison a nuclear power plant with the same peak generation capacity would cost around 12 billion, a combined cycle gas plant would cost 3 billion, a coal plant interestingly has capital costs higher at around 8 billion. Multiple references come to similar numbers, these are not picking biased estimates but looking across a range of well referenced data sets.
Adding in the capital costs of both pumped storage and wind or solar generation together in a system to deliver reliable and consistent power year round, the magic number is on par with coal or nuclear just for the capital costs. The lower annual operating expenses and marginal cost of the power delivering much higher returns on investment compared to the conventional plants.
Having lower ongoing costs than any of those alternative generators and a marginal cost of the power orders of magnitude lower, lower capital costs for peaking plants, why is this discussion continuing?