I know what Chas means. Personally, I don't think that gearboxes were a FIAT strong point! There are several different gearboxes fitted to the Uno. The most common type has the cadmium-plated (gold-coloured) cover on top, and vertical rod/bellcrank at the back with a link across the top - that's similar to the FIAT 127 gearbox of long ago. It's OK but not great. The gearlever has a bendy feel and the synchro on third gear wears out easily

This gearbox hung around until 1992 in both 4- and 5-speed versions, so most models had it, except for the Uno Turbo. The gear linkage has two long rods under the car that can sometimes fall off the ball pins onto which the red or white plastic sockets are pressed. The main cause of great slackness at the lever is the U-shaped clevis which the lever twists and pivots forwards/backwards in. Replacing those bushes and adding some washers makes the biggest difference (on some cars, the lever ends up in the seat padding by the time you get second gear).
The Uno Turbo came with a gearbox from the FIAT Strada which is also similar to the FIAT 128 (so again, another old design not really up to the standard of the latest 80's designs

) This gearbox is identifiable by the single selector rod entering the gearbox at the bottom (hence, 'bottom linkage') which has a concertina-bellows rubber boot. I have seen this gearbox fitted to late ('8

Mk1 70 models (such as your 70SX Chas?). The gearchange feels a bit more robust than the other type - less bendy - and the gearbox is a bit stronger (synchros and bearings last longer).
Both these gearboxes described so far have a stronger synchromesh design (baulk ring) on 1st and 2nd compared to the other gears (Porsche ring). That is the main change compared to the 70's designs (127, 128 etc) from which these gearboxes were derived (the original designs had Porsche ring synchros on all gears and 2nd wore out easily - 1st was often completely useless). In my experience, a worn Porsche ring synchro produces a crunch when it can't cope with the speed difference, where a baulk ring synchro simply won't engage until the speeds match (hence, 'baulk').
At last in the late 80s, FIAT designed a better gearbox from scratch (presumably for the new Tipo) and this turned up in the Mk1 Uno Turbo from 1988 and the Mk2 Turbo and 70 models. The identification of these is the two (or in the Tipo, three) thin selector rods running across the top of the gearbox (from a bellcrank attached to the steering rack mounting) to a selector on the top of the gearbox that twists and lifts. This gearbox seems much stronger than the others, though the gearchange is heavier and more 'clunky' (that also makes it more positive). I am not sure but I think all synchros are of the baulk ring design. Bearings seem to last longer than in the other gearboxes.
There is also another new 'small engine' gearbox from 1992 fitted to the FIRE engines - this is the type where you push the gearknob down (or in the Punto, lift a collar) to select reverse. I think this gearbox has a slight let-down in the gear linkage department - it uses a cable as well as a rod - which gives it a notchy feeling, but I have driven some Punto models when brand new, with this gearbox, and they were good, so I suspect a cable replacement or rod bush replacements will restore good selection. Note there is also a cable for the reverse-gear lockout.
I think this 1992-onwards gearbox is still in use in current FIAT models... I don't think the Italians change gearbox designs unnecessarily... it would be nice if they made a gearbox with synchromesh on reverse gear, as some German manufacturers have had for a long time.
Right, none of this actually answers the question, so here we go. Since reverse has no synchromesh on any of these gearboxes, it's hard to select reverse if the car is moving even slightly or if the clutch does not fully disengage. Therefore I think you must check the clutch operation first - does the cable need tightening or the hydraulics need bleeding? In other words, does the clutch engage near the top of its travel (normal) or right on the floor?
If the clutch really is fine, there must be a mechanical problem in the gearbox and at this point I think you're better off to find a complete replacement gearbox, as the parts are hard to get separately and you might need a number of parts to solve the problem. If you already have a spare gearbox that has some other problem, perhaps it is worth swapping the fork that moves the reverse gear idler (it may be bent), or perhaps the reverse idler itself is chewed.
It is quite normal for reverse to not always readily engage from stationary (if the gear teeth do not happen to line up for the idler to slide into mesh), and this can happen up to 50% of the time (in my experience). The solution is to either release the clutch, then press the clutch and try again, or to release the clutch very slowly while trying to pull the lever into reverse.
I edited the title of this thread, as 'biggaitch' didn't really summarise the thread content all that well.
-Alex