I would say Mobil made the can Jack.
Seeing what mowers went with what brands is interesting.
Most brands recommend Wakefield Castrol (or castrol) at the beginning, off the top of my head the only brands I can remember not recommending Castrol was Rover, Sunbeam (Ampol), Southern Cross (Shell) and Turner (Mobil).
At the beginning of the 60s most brands that still survived turned from Castrol to BP. Pace was strange during this time, it was in a transitional period which saw it go from Castrol (also formerly Wakefield Castrol, which is a very hard can to get), to Ampol and then finally to BP within a very short time.
One thing about that transition is that Castrol was always a specialist, in lubricants only. So the transition was from a lubricant supplier, to the petroleum majors, which were and are suppliers of both fuels and lubricants.
Pope would be a strange one too, it started making its first cans in the mid 1950s, but it wouldn't recommend a fuel brand until it joined Simpson in the early 70s, it would then team up with Mobil.
Its pretty much another huge part of the mower world. I would say most cans would have been made by a petroleum company.
I feel I should make a minor point here, that actual manufacture of the cans would always have been outsourced.
The sheet metal has to be base coat painted, and the screen printed lettering and images applied, before
it is cut into blanks. Which are then formed into can bodies, the long seam soft soldered or 'resistance welded', and the pre-formed ends crimped on.
This process has been the domain of specialised canmaking firms for quite a while. Some food industry canneries did once manufacture cans fully in-house, but even then, their paper labels were usually outsourced to specialist printeries.
Kye, a 2-stroke mower can type you might want to keep an eye out for, is the comparatively uncommon ones that incorporate a metal oil measure. These were always associated with a large screw-on cap - the 20L drum size. Some of them have a normal size cap as well!
The brands I've seen on these include BMS/Lawn Patrol [single cap] and Flymo/Scott Bonnar [dual cap].
Victa never had this feature though; their way was to have volume markings on the inside of the plastic funnels they supplied. So you held your finger against the spout, filled the funnel with oil to the appropriate line, then dumped the oil into the fuel can.
I might still have one of these funnels around; but for sure my old man has a couple, from his 1970s OPE business days.