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 …