You have a 100A supply. That's the most you are going to get. So if your diversity calcs say 166A, tough, you ain't getting a 166A supply however nicely you ask.
I think the reality is you don't have to worry.
I see you don't have an electric shower. If this thread was about adding a 10.5KW electric shower to your house, I don't even think you would be asking the question about a supply upgrade. A 12KW electric boiler is not much more load than that, except of course it will be on for a lot longer.
Personally I think electric boilers are a barking mad idea. People seem to choose them because "oil and gas is so expensive" but have you looked at the price of electricity?
The only plausible reason I can think for fitting an electric boiler is you want it still to "look like" central heating. Otherwise, IF you are intent on heating your house purely by electricity, then individual panel heaters in each room is much more efficient, no heat lost in pipes etc.
Whatever you do, if you have an electric boiler, get yourself onto an Economy 10 tariff. then at least some of your heating will be at the cheap rate. Set the timer to give your morning heat just before the end of the overnight cheap period, and set it again to give a mid day boost during the mid day off peak time.
And do the same with your water heating, heat the tank overnight at the cheap rate, and mid day top up, and you will rarely need to use a peak rate top up.
Horrible though they are, storage heaters are still the cheapest form of electric heating to run. Perhaps use them as background heat and just use peak rate as a top up when needed?
