Ok, so the energy requirement is
12kW * 24H = 288kWH per day.
In your area, say postcode TA6, the online calculator
https://www.pvfitcalculator.energysavingtrust.org.uk/ suggests that a 10kWpeak array at 30degrees mounting angle, facing due south, will achieve approximately 7TWH/year, or about 19kWH/day.
Given that you need 288kWH/day, you'll have to install a 155kWpeak solar array. If you choose 20% efficient solar cells, and find a super cheap supplier/installer, or DIY, then you're looking at about 0.8GBP to 1.25GBP per watt, and about 200 watts per square meter of installed panels:
Cost: 155,000W * 0.8GBP to 1.25GBP = 124,000GBP to 194,000GBP
Area: 155,000W / 200w/m2 = 775 square meters, or a 28m x 28m area, with around 480 solar panels
The solar day is, on average, about 1/3 of a full day, or about 8 hours, so you'd only have 8 hours a day to capture your solar, and the batteries would have to store and then dole out the remaining 2/3.
288kWH * 2/3 stored = 192kWH stored
5kWH batteries are available for around 1,300GBP each:
192kWH / 5kWH * 1,300GBP = 49,920GBP
You will only need a 12kW inverter, and those can be had for resistive loads, like your heater, for under 2,000 GBP. However, you'll need many MPPT battery chargers that will handle 288kW total. A cheap 5kW mppt charge controller should run you about 350GBP, so:
288kW / 5kW * 350GBP = 20,000 GBP
Conclusion:
To run your 12kW heater 24/7 on solar power located somewhere in southwest UK with solar panels tilted at 30 degrees facing due south you'll spend at least 270,000 GBP on solar panels, an inverter, batteries, and solar charge controllers. The installation racking, wiring, mounting, fixtures, and any other parts of the system will add on to that cost.
Further consideration:
Electric heat is 100% efficient. Heat pumps are up to 500% efficient. A 4 ton heat pump is nearly equivalent to the 12kWH heater in terms of heat output, and I expect you can get a biomass heat pump system for under 20,000GBP. It would easily cut your solar requirements in half or more, saving 135,000GBP.
Further, solar water heating is 2-3 times more efficient in turning sun into heat than a solar --> electricity --> heat system. Using the water tank itself as the energy storage you can completely eliminate the batteries, inverter, and charge controllers and simply heat the water using solar water heating panels.
As others have pointed out, your question doesn't provide us with enough information to further optimize the solution. Rather than telling us the solution and asking for numbers, describe the problem fully. This may allow us to suggest alternative solutions, or find areas where your solution might be overkill or insufficient to solve the problem.
Lastly, it's generally more cost effective to optimize your energy usage before changing it to another energy source. The above solution might solve your problem, however if by adding a little insulation you increase your system efficiency by just 10%, your cost drops by 27,000GBP - and the insulation costs far less than that. So understanding what the system is, how it's currently used, all the energy sources and sinks, usage patterns, location, etc we may find opportunities to reduce your solar needs significantly at a lower cost or with a higher environmental impact, depending on what you want to optimize for.
