A check of my reference library confirms that the Thorneycroft Carbine was indeed patented in on 18/7/1901, and Ian Skennerton’s The Lee-Enfield Story has a photo and a brief write-up on page 89.
It’s not strictly a Lee-Enfield (the only similarity is the barrel and the calibre), so technically it’s a totally different rifle.
Indeed, the bolt is behind the trigger and the magazine is in the butt. There’s a safety catch on the right hand side above the trigger, and the guns were trialled for British Army use between 1901 and 1903, when they decided just to shorten the Charger Loading Lee-Enfield by 5 inches (creating the SMLE) and be done with it. Looks like your memory wasn’t playing tricks on you after all! 