I was pleasantly surprised to see prices quoted in £GBP - the Powerwall is available in the UK! But, we don't have enough sunlight here to run a typical house off-grid year-round, do we?
In the UK we get about a quarter of the incident energy from sunlight in Winter than we do in Summer. You could do it by overbuilding your solar array by 4 times over what's required in Summer. That might actually be reasonable if solar prices carry on going down. Or you could do it by having some sort of micro-CHP system which produced electricity and then uses the waste heat to heat the house.
But, yeah, I think this is the major outstanding issue with renewables at the moment. Solar with battery storage looks like it will get parity with the grid anywhere near the equator, where you don't need seasonal storage. The UK needs additional solutions. I think we should be putting more money into developing micro-CHP personally. British Gas were trying out a Sterling engine system a few years back, there are also some in development using Fuel Cells.
In the UK a lot of people are on tariffs which pay them above market rate for the electricity they generate regardless of whether they feed it into the grid or use it themselves. A battery like this will allow them to both sell and use 100% of what they generate.