Don't ya just love those non-standard "corner-case" standards?

This is the primary reason I'll probably never own an old Raleigh or French bike. Far too many of them use obsolete or proprietary standards for some parts that eventually may need to be replaced due to normal wear and tear.

If the cups are still good, you may be able to replace the spindle with a 5- or 7-series JIS square taper spindle - if you can find one with the correct length - and use 15/64" or 6mm bearing balls. If you haven't already seen it, the following link from the late Sheldon Brown describes the process:

https://www.sheldonbrown.com/raleigh26.html#cotterless

That link says a 7-series (for a 73mm BB shell) JIS spindle with 6mm bearing balls seems to work best, but that a 5-series (for a 70mm BB shell) spindle can sometimes also work (but needs to be checked carefully for proper bearing location on the spindle after assembly).

Disclaimer: I've not tried this myself. But the source is generally considered credible.

I'd recommend you start looking. The 5- and 7-series square taper spindles are getting somewhat hard to find, and yours IMO is pitted badly enough you may need one in the not-too-distant future. Plus, the longer you use that pitted spindle the greater chance you have of trashing the cups; the pits will shed metal flakes that over time will act as abrasives to the entire BB - including the cups.

FWIW: Sunlite/YST still makes a threadless bottom bracket if you end up needing to go that way (available at Amazon, Modern Bike, others). But I believe they're designed for a 68mm BB shell, and I don't know if they'll work with anything wider.

Best of luck in finding what you need, and with the bike in general.

This may work, but not well or for long.
Smaller balls will change the contact angle, making it less in line with the principle forces (radial for pedaling, not axial for locating the axle), so increased wear and chance of failure.
Which of couse also means the ebaring tracks will be higher up on their curves, and that portion of the axle/cup may not be finished.

I agree that the Sheldon Brown suggested method is not optimal - but it might work well enough as well as be affordable.

It's true that the bearing tracks may move a bit. But the difference in bearing ball diameter is rather small (<0.397mm, or <0.016"); Raleigh 26TPI cups also reputedly have a somewhat smaller ID than other brands. So I'd guess the bearing geometry shouldn't change all that much.

It also may be the only economically viable alternative.

I presume the OP has verified that his BB cups are Raleigh-proprietary 26TPI cups; he's indicated his BB shell is about 71mm in width. If so, I believe his cups and spindles are long out of production; plus, as noted above the ID of Raleigh 26TPI bearing cups reportedly is somewhat smaller than other manufacturers' BB cups of the era. Suitable exact replacement BB cups or spindles are thus likely not available or will be vintage NOS and expensive as hell.

Other than using a currently-available spindle, available other options are likely to be either very expensive (find NOS in correct length; Phil Wood, if they're even still made for 26TPI Raleigh; or maybe another BB with removable 26TPI mounting rings - perhaps IRD?; re-threading the BB shell) or using a threadless BB. The last might or might not eve be viable; Velo Orange has discontinued their threadless BB (which was known to work in a 71mm shell), and I've not seen any accounts indicating whether or not Sunlite/YST threadless BBs made for 68mm shells will work.

In the OP's situation, if the cups are good I personally would likely give what the late Sheldon Brown suggested a try. His suggestions and opinions were generally good ones, and in this case might be the only economically viable solution.

Different set of issues if the OP's frame has a 24TPI tpi BB shell. Then the problem becomes finding a spindle (and perhaps new cups, if his cups are also trashed) that will work with his wider-than-normal 71mm BB shell. The OP indicated his existing spindle is marked 5SS. If his cups are good and are in fact 24TPI ISO or BSC threaded, since he's in Italy he may be able to find a 5SS spindle and use that as a direct replacement.

His serial starts with W; the probability of 26tpi is close to zero.

If there is any doubt, a known 24tpi cup will mesh with another 24 tpi (as it should), but will rock back-and-forth when a mesh with 26 tpi is attempted.

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...I don't know how far you want to get into this. I looked at your spindle photos. I think in your place, I would probably just maybe smooth out the spindle pitting a little bit with abrasive, check the interior of the cups to make sure there was nothing in there that looked like it was really bad, reassemble with new bearings and grease, and ride the thing. You can measure the spindle really well before you reassemble it, and maybe look for a replacement online or elsewhere, as a passing part of the hobby. In the meantime, you can still ride the bike, and it will doubtless work well if you have the BB adjusted to spin freely.

There is a more labor intensive fix for this (if it is, indeed, Raleigh proprietary threading,) and it requires some more expensive tools. Most people who build or repair frames will have these tools, and you do live in Italy. You can't swing a cat in Italy without finding some old guy who used to make steel frames. I don't know what has happened there, to all that local industry in frame building, but I suspect if you look around, the remnants of it are still around somewhere.

The fix involves modifying this Raleigh frame, by facing down the BB shell from the current 71mm, to the Italain standard 70mm. Then you ream it out a wee bit larger in diameter, to accept Italian threading, and use a set of piloted taps to rethread the shell to Italian. There are still plenty of Italian threaded sealed unit BB cartridges being made and sold. So you just buy one of those in the correct spindle length for your chosen crank, install it, and you're good to go for a long, long time.

But this might be overkill, depending on which Raleigh bicycle this is. Meanwhile, while you decide, just clean, grease, usen new bearings, and reassemble. It will probably go that way for quite a while, and it's a very cheap and easy fix. People tend to get sucked down into distractions on projects like this, which don't necessarily yield a significantly better result.

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...lastly, there are many UK posters who have previously stated on this forum that they simply ran a set of standard threading taps through a Raleigh threaded BB shell, and installed a standard threaded sealed unit bottom bracket cartridge. They report good results. I think this works because even though the new threads you cut doing this are not perfect, a sealed unit BB has its bearings and races internal. So there's not nearly as much force applied to the BB shell threads as you would have in a cup and cone, loose ball assembly. The shell threads only serve to position your bearing assembly in place. Indeed, the things that position the unit are often made from plastic (sometimes aluminum), because of this.

But all this presumes you have Raleigh threading, which you might not. You need to check that out first...you can use a standard threaded RH threaded cup as a tool, to check the threading on the non drive side of your shell.

I was wondering about that. If it's a higher-end Raleigh, it should indeed have a 24TPI BB.

Unfortunately, the OP didn't indicate what model Raleigh he had and I didn't want to assume. His reference to the Sheldon Brown site and apparent willingness to re-use his existing spindle though pitted also led me to believe - perhaps wrongly - that he'd already determined that he had a Raleigh-proprietary 26TPI BB and didn't have too many other good options.

If the OP's BB is in fact threaded 24TPI, I'd guess he shouldn't have much of a problem finding a replacement spindle. He's indicated his existing spindle is marked 5SS, which I believe should be 32/55/37.5 - and he's in Italy. Only issue I'd foresee might be finding one that's JIS if that's the taper he needs. I'd also guess he shouldn't have much problem finding a set of replacement BSC or ISO cups if necessary, either.

"5" series spindles normally fit 70 mm Italian bottom brackets, also 68 mm French with thin cups.

https://www.sheldonbrown.com/bbsize.html

Thanks all; I've been out of touch for a while. I'm going to go with reassembly with new bearings for the time being and see how that goes, while thinking about the other more intricate fixes.