If it is similar to many of the axles I have seen, it should not be hard to duplicate by a competent machine shop. I suspect it has splines on one or both ends so the shop needs to be able to handle that or at least sub that portion out. As far as material I would ask them what "shaft stock" they recommend, then check its properties.

Sorry, I just re-read your post and determined you are not talking about the specific axle shaft but a whole differential or trans axle assembly. Probably due to a difference in what country we are from even though we are both communicating in English. Sort of like a tyre or tire.

I think he is talking of the skin, not the innards

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It all depends on how original you want the car to be.

ebay U.K is where I'd be lurking, or contact one of the many Rover owner car clubs in the U.K.

Being in Spain, it wouldn't be so hard to go to the U.K. for a weekend drive to collect it or get it freighted to you. Bit harder for me in Australia.

Alternatively you could adapt a more modern rear axle to the car. Plenty of different makes and models to choose from. Looking at the size of it from a photo on the web, maybe a Datsun 120y axle would be close to size. Maybe some thing from an early rear drive solid axle Fiat? Volvo PV series, perhaps 1 or 2 series but you'll have to do some work to fit it. I've got lots of different cars I could choose from locally here, but not sure if you have had the same cars there.

Photo of 1921 8 hp rover I'm looking at here

http://www.rover-v8.nl/dutchroverarchives/index.html

You don't mention if it has a torque tube connection to the gearbox or if it is the conventional prop shaft arrangement.

If it is a 4 cylinder car then a axle out of a similar car will do. Your main dimensions to compare with are;

Overall width. From end to end

Spring mounts. The width between the spring mounts. And the width of the mounts.

The number of wheel studs.

The PCD or pitch circle diameter of the studs.

Brake types. If your car has drums or disk(maybe not for 1921), and is it a hydraulic brake?

Gear ratio may be important too though most 4 cylinder cars are around 4.11:1.

Rule number 1 for tinkering with old cars (and new ones too) "Fun costs money! How hard do you want to laugh?"

We really need more information to help you here, and what is your intention with the car?

Is it for historical restoration or for personal amusement where the "correct" parts are not so important?

Hope this helps you.

Do you have any photos of the differential?

Which parts are missing?

A good machine shop can make gears to suit, and even figure out what is missing and make those parts too.

Now days they can design on computer, and make parts on an automated milling machine.

When you contacted Rover what was the nature of reply?

Try contacting the Rover Sports Register, they may know someone close to you who can help.

Is this what you are look for parts for?

http://gallery.brit-cars.com/showphoto.php/photo/5391

Ask on their forum.