Louie is the one to trust on this one, as he actually has a 1.0 i.e. himself
The lag when pulling away may be standard behaviour, it's hard to say. Is it worse than it used to be?
I think that the throttle switch on the carburettor could cause this problem (?) There is a switch that should click when the throttle is closed. Probably worth checking this first, as it doesn't cost you anything to clean/adjust the linkage and it would be a logical explanation for a fault that just suddenly appeared.
The purpose of the switch is that it tells the ECU to halve the frequency of the injector pulsing (prevents over-fuelling when idling).
Another possible sudden fault would be a vacuum leak - e.g. in one of the various rubber hoses. I think the distributor will have a vacuum advance unit (round capsule on the side) and these are a common failure. You can test it by sucking on its rubber pipe (but clean the pipe first

) - it should not be possible to draw air through. If you can, it means the engine will be, causing the idle to be erratic and pulling away will also be a little more lumpy than usual.
You are right about the idea of cleaning - the single injector can be removed and cleaned ultrasonically by a specialist - they can also test the spray pattern. If you can afford to be without the car for a day or two, I think that would be more worth the money than a bottle of injector cleaner poured in the tank (it would be hard to judge the effectiveness of the latter). A cleaned and efficiently-spraying injector may save enough fuel in a year to pay for the cost of cleaning...
The other item to clean (by replacing) would be the fuel filter, but I don't believe this would cause a sudden deterioration so it would be fairly well down on my list of priorities I think. Also fairly low on the list would be the fuel pump (in the tank, I believe) - may need changing - that will cost you money to get second-hand, but at least you can do the job yourself (it's under the back seat under an access cover). It probably has some sort of pickup screen which you can inspect first - maybe that just needs a clean?
Before you do anything with the fuel pump or filter, it may prove more cost-effective to have a specialist check the fuel system pressure with a gauge. That may then point you in the right direction. I suspect that since it's an electric pump, the pressure will be constant at all times. Thus if it was low, you'd be having problems at high speeds (well, Uno 45-high anyway

)
-Alex