How early is the Lee Speed? Is it based on the LE action or SMLE action?

I have a Martini Sporting rifle sold by Rawbone, proofs and marking indicate it is 1890's gun and it is marked, "for .303 Ammunition" It is also mark as using Rifleite powder. (is there a modern equivalant?)

It chambers a .303 British cartridge and will blow the head right off if fired. Bore slugs 304 major (groove) diameter. It does not use a .311 bullet.

When the Brits first started working this cartridge they were working with the Swiss Rubin cartridge which used .303 diameter bullets at the time.

Hawk .303 diameter 180 Bullets work just fine in this rifle.

I was wondering if Lee Speed went back as far the early 1890's?