Here's my understanding of things:
Birmingham Small Arms (BSA) were happily building MLM Mk.I rifles during the late 1880s, when the new pattern (Mk.II) appeared, approved in 1890.
Unfortunately, Govt delays went on for a couple of years, with BSA waiting for the contract. During this time there was considerable pressure to release a sporting rifle on the MLM action for the 'new' .303 cartridge, so in 1992 BSA lost their patience and released a sporter on the Mk.I action. To sever any ties with the official military pattern, these rifles were marked "Lee Speed Patents" on the ferrule (often with BSA&Co as well), and sold initially for 6 pounds 10 shillings. They are the rifles we now call Lee Speeds.

Concurrently, BSA and LSA continued to make a 'Service Pattern' rifle for civilian use, which sold for 4 quid. When the Mk.II contract was finally awarded, civilian versions of that sold for 5 quid. These rifles have BSA&Co or LSA&Co on the ferrule, without the 'Lee Speed Patents' wording.

The Lee Speeds proved popular, and hence were made continuously up to at least 1912, and probably to the beginning of WWI. Three grades (patterns) were offered, with a number of options including 10-round mag at no extra cost, swept-forward flattened bolt handles on the No.1 and No.2 patterns, and tangent sights. Optional extras included the Metford Mk.II bolt (no cocking-piece safety), long barrel (up to 30 inches!), trap butt-plate with oil-bottle and pull-through, and Metford rifling (at least until 1912).

Other civilian versions of the service rifle, through its various numbers and marks, were made up by BSA for sale or release to the trade virtually continuously till the end of Lee Enfield production. The latest one I know of personally is my ~1950s Churchill sporter on a 1945 Ishapore No.1 Mk.III action, but Parker Hale variants probably made it into the 1960s.

Authors like Skennerton, Linney, Faris etc have no trouble identifying Lee Speeds from the various MLM and MLE sporters around at the time. Sporting service-pattern rifles are simply not Lee Speeds. I never like to say 'never' where the British gun trade is concerned, but all Lee Speeds will have 'Lee Speed Patents' on the ferrule, unless it has been removed. If not, its not a Lee Speed.

BTW, I did receive your PM a while back, it hit my desk at a busy time and I wanted to dig out my research before replying. I wish there were more days in the week. Any extra would simply get soaked up by guns and shooting, though!