We've got a solar array and storage battery
Are these meant to keep the house running for a short while if you get a power cut? Mine don't seem to be able to do this.
No, that's the downside of the way the existing legislation and technology works. If your solar array is connected to the grid, it must shut down if there's no power on the grid. It's to protect engineers who might be working to fix any problem.
It is possible to get a setup that does provide power when the grid is non-operational, but they are a lot more expensive than a normal installation.