sorry, not meanting to hack you off.
It takes 9,5Kw to heat 180l of water by 45deg multiple that by 365day and you cab see you need about 3500kwh to heat hot water in many houses. Not sure how the government got to a 2400 watt figure from as it is not my experience. We personally run our boiler at 55 deg for instance.
The assumptions you are making mis-understand those used in SAP and other calculations of hot water usage.
SAP is based on a usage temperature of 47degC which is on the high side. Most hot water is used for showering. Get in a shower at 47 deg and you will get out again bloody quick! Most people shower between 38 and 42 deg. Anything above this is pretty uncomfortable. Humans are very sensitive to contact heat above body temperature. There is also an inherent assumption that water is heated to 60deg for Legionella disinfection.
Calculation of daily hot water consumption is still open to debate. The calculation in SAP2005 was based on 25litres a person plus a 36litre overhead. Your 180litres is enough by this calculation for 5.76 people. SAP2009 and draft 2012 both use a calculation based on floor area. This came about from a survey that showed the average occupancy of a domestic dwelling is 3.1 people. An algorithm was then built to reflect this. Whilst this may be OK for the general purposes of SAP, it is completely bonkers for use in planning/designing domestic heating systems or renewable heating systems. The Draft of the revision of MIS3001 'Requirements For Contractors Undertaking The Supply, Design, Installation, Set To Work, Commissioning and Handover of Solar Heating Microgeneration Systems' goes some way to address this by allowing use of the SAP2005 formula if average occupancy is known. Practical experience suggests that this still understates usage. I personally work on 40 litres per person with no overhead.
These parameters can then be input into the SAP hot water energy requirement. This is seasonalised to take into account variance in water inlet temperature and usage. Using the parameters you state gives a figure of 3450kWh. However, using the SAP2005 usage formula and the SAP standard temperature gives 2145kWh. Using what I consider more realistic parameters (4 x 40ltrs @ 45deg) gives 2387kWh or to more closely align with SAP (4 x 40ltrs @ 47deg) gives 2523kWh. As such you will see that the given figure of 2400kWh is entirely justified.
This is based on usage and not storage volume. This can make tank sizing a black art when taking into consideration heating to 60deg (required in solar thermal standard), standing loss from tank, and pipe losses. As alluded to the simple act of replacing a tank leads to increased savings due to reduced standing loss.
Blithely
selling or fitting an Immersun or other proportional controller without taking in to account the factors outlined in my original post is doing no one any favours. The purpose of this thread was to generate constructive comments on how to better what I had already put together to allow evaluation.