There were actually several successful automatic and semi-automatic SMLE conversions, though you are right in the fact that none of them saw real mass-production on the scale of other early machineguns.
Howell Automatic Rifle
Calibre: .303 in
Rifling & Twist: 5 Groove, Enfield, LH
Barrel Length: 25.2 in (640mm)
Overall Length: 44.5 in (1130mm)
Approx. Weight: 11 lb 12 oz (5.3kg)
Magazine Capacity: 10 or 20 rounds
Converted: Base Workshops
The Howell Automatic Rifle was developed during the first World War in Britain, and reappeared early in the second as a means of conversion to automatic weapons for issue to Home Guard and for anti-aircraft use. Conversion to a Howell was permanent and could only fire in full automatic.
Reider Automatic Rifle
Calibre: .303 in
Rifling & Twist: 5 Groove, Enfield, LH
Barrel Length: 25.2 in (640mm)
Overall Length: 44.5 in (1130mm)
Approx. Weight: 11 lb 8 oz (5.2kg)
Magazine Capacity: 10, 25 or 30 rounds
Converted: The Castle, Capetown
The South African Reider Automatic Rifle was produced in 1940-1941 and was a more modular design which could be 'dropped in' to the rifle and later removed without harming the rifle - the bolt was not modified. The last conversions made in mid-1941 were of a more refined design but the whole concept was shelved in 1941 when nobody particularly wanted to adopt the rifle attachment. The Reider was also capable of semi-auto fire.
Charlton Automatic Rifle
Calibre: .303 in
Rifling & Twist: 5 Groove, Enfield, LH
Barrel Length: 26 in (660mm) including compensator
Overall Length: 45.5 in (1156mm)
Approx. Weight: 16 lb (7.3kg)
Magazine Capacity: 10 or 30 rounds
Converted: Charlton's Motor Workshop
Now the Charlton Automatic Rifle you already mentioned, but it was actually originally developed in New Zealand, not Australia. It was a stop-gap light machinegun and was made from Lee-Metford rifles mostly, Lee Enfields only being used when the L-M's were all used up. It was designed to ease the lack of available Bren guns somewhat, and can accept the 30-round Bren magazine.
Charlton Automatic Rifle, SMLE Model
Calibre: .303 in
Rifling & Twist: 5 Groove, Enfield, LH
Barrel Length: 25.2 in (640mm)
Overall Length: 45.6 in (1158mm)
Approx. Weight: 11 lb 8 oz (5.2kg)
Magazine Capacity: 10 rounds
Converted: Electrolux, Australia
An Australian version of the Charlton was also produced, the Charlton Automatic Rifle, SMLE Model. This is the model you are thinking of, Max. This was made from the more recent SMLEs which actually helped fix a few problems the Kiwis were facing with their Charlton design. These look a lot neater than the NZ version aswell, more enclosed. These were designed to take the 10 round SMLE mags but not the Bren, for whatever reason. In addition to being neater, it was also much lighter.
Howard Francis Self-Loading Carbine
Calibre: 7.63mm Mauser
Rifling & Twist: 5 Groove, Enfield, LH
Barrel Length: 12.75 in (324mm)
Overall Length: 32 in (812mm)
Approx. Weight: 8 lb 1.5 oz (3.7kg)
Magazine Capacity: 12 rounds
Converted: Prototype Only
A very interesting one is the Howard Frances Self-Loading Carbine, a conversion from a No. 1 Mk III SMLE to the 7.63mm Mauser pistol cartridge. It fired in semi-automatic only. Suffered some feeding and extraction problems and, despite meeting accuracy and soundness of design concept, never made it past prototype stage. Very light and very short little carbine.
Phew! Bear in mind a Pederson device was also developed for use with the SMLE family of rifles. I hope that information is of some use to someone