How big a solar battery do I need to store *all* my home's electricity?

I have a modest set of solar panels on an entirely ordinary house in suburban London. On average they generate about 3,800kWh per year. We also use about 3,800kWh of electricity each year. Obviously, we can't use all the power produced over summer and we need to buy power in winter. So here's my question: How big a battery would we need in order to be completely self-sufficient? Background …

Terence Eden’s Blog

Author’s diagram is about summer. Fall, winter, spring is about heating-degree days. If you’re heating your home with electricity, you’ll not get there with batteries.

So, working towards a solution, there are other ways to store excess energy than in batteries. One example is sand, which can be heated to very high temperatures. Insulate a sand container well and its storage can do a lot of home-heating.

Example: livescience.com/…/a-scalding-hot-sand-battery-is-…

We’ll need to put a lot of different methods into use. There are many practical ideas out there, and they’ll need to be tried.

A scalding hot 'sand battery' is now heating a small Finnish town

Engineers create a sand battery that they say will slash the carbon emissions in Pornainen, Finland, by 70% — it uses renewables to heat the sand to almost 850 degrees Fahrenheit.

Live Science

The sand storage is used for district heating. It’s not much of a substitute for single homes that have electrical heating or are off-grid.

It’s a great way to balance both the electrical and the heating grids so that more electricity from renewables can be used to offset other means of heat production, but it needs to be done by the district heating supplier. I doubt it makes sense for individual houses.

When I was a kid my parents had electric resistance heat with some very effective thermal storage.

Each room had a unit about the size of a typical radiator. The unit was basically an insulated box with a small circulation fan. I’m not sure what was inside but always assumed some form of brick - they weren’t expensive so it couldn’t be anything exotic. At night when electric rates were low, whatever was inside the units was heated up. During the day, the only power usage was a small circulation fan controlled by the thermostat.

I just got a heat pump installed and thought thermal storage would be worth considering, but contractors acted like they never heard of it, and there really didn’t seem to be any consumer units available.

Very old heaters used to contain lots of asbestos. It might have worked well.

Not that old, plus I don’t see it.

Asbestos is great at insulating really hot things so was used on boilers , especially ships and industrial to insulate the hot pipes and improve efficiency. However in this case we need something with thermal mass: any sand or rock might do, or water, or oil, or a modern phase change material. That material next to the heater will get hot but the entire mass won’t, so can be insulated with standard materials. There’s no point in something like asbestos

An important part of my point was also that what I assume were cheap materials was enough to take advantage of nightly time of use metering. In upstate NY, a standard “radiator” per room was sufficient, similar to hot water or steam heat

These are called “storage heaters”. They’re still available. www.which.co.uk/…/storage-heaters-aokoz3G2Em9L
Storage heaters explained - Which?

What you need to know about storage heaters, including how much they cost and if night storage heaters could save you money on your energy bills.

Which?
Yep, those look familiar. However for heat pumps I found one manufacturer in Canada plus a few experimental things

Yep, those look familiar. However for heat pumps I found one manufacturer in Canada plus a few experimental things

While I don’t have timebof use metering, I was looking into solar and it could be really useful for shifting the load so solar does most of the heating