= Solution
The Shockley-Queisser calculation treats a <single-junction solar cell> with a single <band gap>, in steady state, with one collected <electron-hole pair> per absorbed above-gap photon, an ideal absorption edge, thermalized carriers and <radiative recombination> as the limiting <recombination> process. The source spectrum, cell <temperature>, angular acceptance and optical concentration must be specified. Below-gap photons are transmitted; <energy> above the gap is lost during carrier <thermalization>; the cell must emit photons by <detailed balance>, producing a <recombination> current and an entropy-related voltage loss. Delivering <power> at finite current also puts the operating voltage below the <open-circuit voltage>. <Nonradiative recombination>, resistance and imperfect collection worsen a real cell but are not required for the ideal limit.
Three ways to change those assumptions are <tandem solar cells>, which divide the spectrum among gaps and reduce both transmission and <thermalization> losses; <hot-carrier solar cells>, which aims to collect excess carrier <energy> before <thermalization>; and <carrier multiplication> or spectral conversion, which aims to use a high-energy photon for more than one excitation or combine otherwise unusable sub-gap photons. These concepts have additional practical losses and do not automatically outperform an optimized conventional device. The usual unconcentrated single-junction optimum is approximately one third under a terrestrial solar spectrum, rather than a universal efficiency independent of illumination.
For the geometrical estimate, take the stated horizontal equinox irradiance to set a constant direct-normal reference. The equinox solar-noon elevation is $\alpha_e=90^\circ-51.75^\circ=38.25^\circ$, so this reference is $I_n=1/\sin\alpha_e\simeq1.62\,\mathrm{kW\,m^{-2}}$. A south-facing panel with tilt $\beta=41.1^\circ$ has noon incidence factor $\cos(51.75^\circ-\delta-41.1^\circ)$, where $\delta=\pm23.44^\circ$. Relative to the $1\,\mathrm{kW\,m^{-2}}$ plane-of-array rating,
$$
\boxed{P_{\rm June}\simeq5\frac{\cos12.79^\circ}{\sin38.25^\circ}=7.9\,\mathrm{kW},\qquad
P_{\rm December}\simeq5\frac{\cos34.09^\circ}{\sin38.25^\circ}=6.7\,\mathrm{kW}.}
$$
These are the results of that \b[idealized geometrical <normalization>], not credible seasonal production forecasts. Its inferred direct-normal irradiance already exceeds the approximately $1.36\,\mathrm{kW\,m^{-2}}$ <solar irradiance> outside the atmosphere, so the supplied horizontal benchmark cannot describe a purely direct noon beam literally. Real direct and diffuse fractions, atmospheric attenuation at low winter elevation, cell <temperature> and inverter clipping are unspecified. An alternative assumption of $1\,\mathrm{kW\,m^{-2}}$ direct-normal irradiance gives approximately $4.88$ and $4.14$ kW. A physically unique maximum cannot be inferred without an irradiance model.
The stated annual output corresponds to $4100/5=820$ full-rated hours, an average <power> of $0.468$ kW and a <capacity factor> of $9.4\%$. Night, cloud, seasonal day <length> and other losses explain the large difference from an instantaneous sunlit estimate.
For a national scale estimate, take UK area $2.44\times10^{11}\,\mathrm{m^2}$, population $6.6\times10^7$, and annual mean solar input $100\,\mathrm{W\,m^{-2}}$. Covering five percent with twenty-percent-efficient modules gives
$$
\boxed{\frac{E}{N\,\mathrm{day}}\sim
\frac{0.05(2.44\times10^{11})(0.20)(100)(24)}{1000(6.6\times10^7)}
\simeq89\,\mathrm{kWh\,person^{-1}\,day^{-1}}.}
$$
This is comparable with an order-$100$ kWh daily per-person primary-energy budget, and much larger than electricity use alone, of order $10$-$15$ kWh per person per day. It is a gross area-and-flux estimate: access land, shading, seasonal storage, curtailment and conversion between <primary energy> and electrical end use all affect its interpretation.
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