https://flashbak.com/wp-content/uploads/2021/04/Routemasters-in-Park-Lane-with-RM1240-nearest.-3rd-April-1976.-1200x811.jpeg
Does anyone have any information as to what type of lantern this is?

They Don't look like the atlas alpha 8 lanterns, but if, hey ho 

I've changed the name of the topic.

According to http://www.simoncornwell.com/lighting/manufact/atlas/fullrange/l1.htm (section "alpha eight"), it may be possible that the lanterns in the photo may have been a prototype that pre-dated the Alpha 8. The applicable quote states:

Originally designed as a special lantern for the Marble Arch relighting scheme at the experimental height of 30'. (This was outside of the specifications at the time but it was one of many experimental installations of high-power lanterns at heights higher than 25' which anticipated the new specification BSCP 1004:1963).

I also found alternate views of the lanterns. The first one is from Alamy, and the other from a eBay listing:

• https://www.alamy.com/the-london-hilton-hotel-in-park-lane-which-was-opened-by-mrs-reginald-maudling-wife-of-the-chancellor-of-the-exchequer-yesterday-18th-april-1963-image623682167.html
• https://www.ebay.co.uk/itm/324742920575

It appears that Thorn Electrical Industries may have been asked by Westminster City Council to come up with more powerful lighting for the Park Lane widening. Unlike the Alpha 8, replacing the lamps may have required removing the bowl, instead of opening the hatch on the top of the canopy.

Yeah, maybe.
It might just be one of those things that's lost in time.