You need some leisure batteries and they will run 12 volt lighting for weeks,
www.12voltplanet.co.uk
www.the12voltshop.co.uk/Shop/
You can charge them up off the mains, one would run lights for a week,
In your case I would have at least two,
You can add a solar panel and it will keep them topped up permanently.
You can get a simple system cheaply, I would have a chat with one of the specialist shops, and explain all your needs,
lots of my friends run entire homes off these systems, so it will be really easy to set up a system for your needs.
There are many websites discussing the various merits of the different set ups,
we have 12 volt, so when we have power cuts life go on as normal, I wouldn't be without it. I run decent LED lights, so the batteries with a solar top up go on for ever.