I don't know offhand of any known brake upgrades for the Turbo, but there are plenty of aftermarket parts available.
If it's stopping power you're after Fro$ty, then the most important part(s) you will need are better brake calipers. Wilwood do reasonably priced 4 pot calipers, but I don't know if any of them are suitable for a Uno.
Often overlooked is the master cylinder. Bigger calipers sometimes need more fluid pushed into them, so a master cylinder upgrade is also worth looking into.
The biggest myth is that fitting grooved or drilled brake discs make better brakes. On their own they don't. In fact, they're often no better than a good pair of vented discs.
What is important is the clamping power of the calipers, also how good the brake pads are themselves and how much of the disc 'swept' area they contact with. Sometimes putting on some quality brake pads can improve braking significantly without changing anything else. The same can be said for just changing the brake fluid, as often it's old and contaminated with moisture and affects the efficiency of the brakes.
But, unless it's for track use only, steer clear from race pads. They only work properly when they are warmed up, and in normal driving that often doesn't happen. Until race pads have heated up the braking is WORSE than normal pads!
A good idea for a possible direct swap is to look at brakes fitted to larger Fiats. Often one manufacturer (eg Fiat) will make brakes to a similar design though they are fitted to different models throughout the range. The bigger brakes will have been designed to stop a larger and heavier car, so in the Uno they should give more powerful brakes.
So how about measuring up the brakes on a Tipo 16V Sedicionovalve? (Not sure if I spelt that right!) Also a possibilty are the brakes from a Strada Abarth 105/ 130TC, though these might be a bit hard to come by but I know they are of a very similar design to the Uno's brakes.
As ChrisUnoman mentioned, Lancia Integrale brakes might also fit. Also possible are brakes from some of the sporting Alfas, as both Lancia and Alfa are owned by Fiat.
What I think you'll be looking at is to get the whole hub assembly, caliper, caliper carrier and disc, and if you're lucky it might well bolt up to the Uno's strut and and lower suspension arm. The only way is to try. You might also need the brake master cylinder, and again you'll have to see if it will fit in place of the Uno's original.
I think in all the above cases though, you'll have to fit 14" wheels or bigger as the discs from all those models are too big to fit the 13" standard wheels. Though I suspect Fro$ty already has bigger wheels fitted so this shouldn't be a problem ;-)
Lastly, before spending large amounts of money on brake upgrades try a cheap'ish and simple upgrade:
Fit braided brake hoses, clean the pistons and sliders on the standard calipers, fit some good quality brake pads and flush through the system with new brake fluid. Quite often that alone will give a significant increase in braking simply by making the brakes work at the top level of their efficiency.
Also yes, compared with modern brakes the Uno does seem to be a bit lacking. But often that's simply because the brakes in modern cars have more powerful servos that reduce the amount of effort when you press the brake pedal, not necessarily because they have much better brakes!
I noticed this when I was given a loan car (a Fiat Punto) while my Uno was off the road. When I went back to my Uno it felt so weak in comparison, but stamping on the brakes would still lock the wheels so it was more a question of brake feel rather than less braking.
Whatever you decide, let us know how you get on Fro$ty. It would be good to find that there may well be a Fiat that has bigger brakes that can simply be swapped into the Uno!
Chas