Hello, yes, brown is a common problem afflicting the base model Unos and the SX (but never the Turbo). At least it's a stylish shade of mid-brown... Did you know they came in grey originally (back in 1984) and brown was introduced later, at the time when other manufacturers were moving from brown to grey...
If it's a series-1 Uno (with the separate instrument binnacle, paddle switches, and one stalk on the steering column), most of the squeaking is probably coming from the two hooks in the bottom corners of the windscreen frame. The instrument binnacle itself, and its lid, is also a cause of squeaks. The best remedy is to take the dashboard main part out (leave the heater in place), separate all the parts (the binnacle is screwed on from underneath) and reassemble with silicone grease between surfaces that touch. Similar advice applies to the series-2 Uno introduced in 1989, except that the dashboard (still available in brown, as well as black) is a completely different design with fewer parts and the top corners are screwed in place.
To remove the dashboard main part, the basic process is to remove the switches and instruments (the lid lifts up at the side closest to the windscreen, then pull towards you), undo screws along the bottom edge (the one in the top centre under a cover is for the heater and need not be removed), remove steering column covers and undo two screws below where the instruments were, and then begin a wrestling operation to lift the dashboard hooks out of the (breakable) metal clips below the bottom corners of the windscreen. It's not really a difficult job if those hooks lift out easily (perhaps the clips are already broken and that's why it squeaks...)
Silicone grease can be hard to find (need an engineering supply shop) but it is important not to use other types of grease (e.g. rubber grease) as those will make plastics brittle.
-Alex