This bracket and lantern was a gift from a specialist in antique lighting. Having found this website useful, and having this bracket spare, he offered it to me for free. Many thanks Jesse.

The lantern turns out to be a very rare variant of the ESLA Bi-Multi Group 'A' Two-Way range. Removing the paint from the lantern's canopy revealed the following:

So:

1. As a rare 180° ESLA it produced straight beams of light in an axial-asymmetric distribution, so it wouldn't have been used for side-of-road lighting. Therefore, as it's mounted on a swan-neck bracket, I believe this lantern would've be used to light a footpath. Additionally, the orientation of the lantern isn't important, which is why it haven't got the PATH and ROAD directions etched on the canopy.

2. The extremely rare circular ESLA logo is used. I've only seen this on one other lantern. Unfortunately I don't have enough information yet to be able to date the lantern from its use.

The bracket (believed to be by Lucy) is also interesting: the ball-and-monkey-tail finial is quite rare, the bracket curvature is non-standard, and the front of the fuse box is fitted with a toggle switch. (Originally a lamplighter would've used a long pole to switch the lantern on and off by this switch).