A slight difference in tyre size like that doesn't matter, though the chains MUST be the right size... if the packaging doesn't say they fit, I think you should return them. Loose chains are very dangerous as they will fling into suspension parts or brake hoses, or undo themselves completely and damage something else as they fly off. The chart on your eBay listing says those chains will be too large for 155/70 13 or 135/80 13 tyres (original Uno sizes). I wish I'd read the eBay ad earlier, but I'm not one of your thin-tyred UK brothers

The smallest size shown is a 155/80 13. You could buy a set of those tyres cheaply enough and they will work OK on the Uno, but I think if you're going to buy tyres, you may as well buy winter tyres - it all depends on your driving environment, though...
As the others have said, chains are a one-off use item, not something you'd leave on the car unless you are only ever trying to drive on deep snow, which I don't think you will be. I'm sure the weather's far too changeable where you are.
Last year I used chains, in the same way as rawill mentioned, to get up the Mt Hutt access road to a skifield. The road is steep, so past a certain point, it's snow-covered. Without chains it was not passable - even four-wheel-drive vehicles are prone to spin a wheel. The chains keep you moving - slowly and safely, under 40km/h-20mph! - even though the back end might slide around (I was driving a Toyota Camry). The vibrations are chronic and will probably shake the car to bits over time (of course, this was a rental car, so no-one cares about that!) After a couple of days, the snow had cleared anyway.
It is quite a fiddle to get chains on or off, so you wouldn't want to be doing that more than once in a journey. I think they are a good idea if you regularly have to drive up a steep hill close to home that gets properly snow-covered. Otherwise, I think you'll be better off with winter tyres. As Chas said, you don't want tyres that are too wide. Winter tyres have a softer compound and more water-channelling capability, at the expense of increased wear in dry conditions. It is common in European countries to have a set of winter and a set of summer tyres, especially now that the German uber-saloons come with such wide summer tyres.
At the end of the day though, whatever tyres are fitted, safe winter driving depends on the skill of the driver.
-Alex