From information that I have gathered over time and images viewed, I believe the majority of M1903, M1905, M1908, and M1910 Steyr built Take Down Models were sold 'through the British trade', many of them with fitted travel cases, yet without a retailer's name engraved on them.

The Steyr factory built takedown system was very similar to that used by Westley Richards, as on this WR Mauser in 1912 advert:

Many authors and sellers have long referred to them as the 'British Take Down Mannlicher' with some insisting that they were 'converted' in England. To confuse matters there were, indeed, conversions done in the land of Big Ben; often of the interrupted screw type (break open) and which often do have a retailer's mark.

The Steyr built MS Take Down Model worked thusly, as described in the 1939 Stoeger catalog:

My own M1910 Take Down Model, proofed 1922, bears no retailer's mark. It does have the British added proofs and stampings typical of MS takedowns of the period such as bullet weight, diameter, and maximum Cordite load. It has a fitted case that has long since lost its inner lid label and was purchased 'second hand' by my grandfather in the British colony of Ceylon in 1930 or 31.

An image swiped from the 'net, detail of an M1905 Take Down Model:

Steyr built MS Take Down Model in 'Army and Navy' (retailer) labeled case:

It seems the market for take down models was primarily to steamship travelers and 'Great White Hunters' or those who fancied themselves so.

M1910 Take Down Model afield.