Gas combi boilers are rated around the 30kW mark so 12kW electric in my opinion won't cut it for a house. You don't specify how big a property you have but only mention it is a house. However you said you have done the necessary calculations and believe 12kW would be suitable. If you have done this correctly ie size of the rooms, thermal insulation of the walls of the building etc etc to find out the total BTUs you need and not just on the number of radiators required then all should be good.
There is no rule regarding half the current ampage but I am pretty sure you would need to upgrade to a 100A main fuse. With no gas you are going to have an electric oven and possibly an electric shower. So you would need to talk to your DNO regarding that and also tell them you are wanting to install a 12kW electric combi boiler.
Given the above you would need to work out your maximum demand to see if the above is possible. Certainly it is possible to install a 12kW electric boiler but if you have lots of other high kW usage equipment, which given you have no gas is very likely, you need to first work out if adding 12kW is feasible, if it is then almost certainly you will need a 100A main fuse so then talk to your DNO about upgrading.
So to recap
1. Work out your Maximum Demand with the 12kW Combi Boiler included
2 If the Maximum Demand is under 100A then talk to your DNO about what you are wanting to install and that you require an upgrade to 100A supply. You can skip this step if MD is under 80A but this is extremely unlikely.
With no gas in the house there is a fair chance your MD will go beyond 100A with 12Kw added the only option then would be to upgrade to a 3 phase supply (£££)
**Update: I checked my Utilita account and use max 12-13kW a day. My house is two bed with solid walls and holds heat well. The fuse panel I have says it's for a 100amp supply, if this makes any difference?
From the above it doesn't sound like you have done the appropriate calculations to size the heating requirements, you must do this properly or you may well be disappointed with the results.
You must do a proper Maximum Demand calculation, the figures you give are likely kWh usage readings, you must have an electrical installation that meets MD requirements.
One other consideration as I don't have access to my books at the moment and I haven't done a design with a 63A protective device (which you would require for 12kW load) with an 80A main fuse, is that if your MD does come under 80A you may still have to upgrade to 100A just so there is no chance of the main fuse blowing in fault conditions. You certainly don't want to have to call out the DNO to restore your power! As I say I doubt you will come in under 80A but if by some chance you do another check is that selectivity between the devices is adequate. This might be the half rule you were referring to in your original question. Your electrician might have said that generally you want the protective device to be half that of the upstream device. Whilst it is not untrue that following this will result in achieving selectivity this doesn’t necessarily apply when you need to do a bespoke electrical design as in your case. I have given you snap shots into the design process for something of this nature to try to give you some guidance but you will need a properly calculated design for this install.
How costly is changing to a three-phase supply? **
From UK Power Networks (2022 prices)
12% of 3 Phase upgrades cost £1,700 – £3,500 (+VAT)
70% of 3 Phase upgrades cost £3,500 – £6,000 (+VAT)
18% of 3 Phase upgrades cost over £6,000 (+VAT)
Many factors will impact on the price.
As CIS London said an alternative to look into is Air Source Heat Pumps they seem to be the in thing at the moment and I think you can get grants for them.