Hello Danny and welcome :wave:
That's a very tidy Uno of yours (in your profile pic). I always liked that 'French' blue.
The first option that springs to mind is an engine transplant from an Uno Turbo into your 5-dr shell, which creates an interesting result. Other running gear, such as brakes, front hubs, driveshafts should be swapped as well, so you'd basically need a rusty/bent Uno Turbo as a donor.
Working with what you have, the 1116cc engine is the same family as the old FIAT 128/Strada/X1/9. There are tuning parts available, particularly in the USA. For example, a 'fast road' camshaft from Bayless, a custom-made exhaust, and a twin Weber 36 DCNF carburettor setup would give a nice rorty snarl - but it could be more expensive than going down the Turbo route!
A cheaper option might be to swap the 1116cc bottom end for a 1498cc bottom end, or even the 1580cc block of a Tipo (but for that, you'd need basically the whole engine as the cylinder head bolts are smaller). Basically, you can mix and match parts to create a bigger engine than your 1116cc, and that doesn't cost too much. The larger displacement versions have a longer-stroke crankshaft which gives more torque ('grunt', better acceleration and even, better economy (the 1116cc is the shortest stroke of all).
-Alex