I don't believe Big W came onto the scene until well into the early 80s. That mower base is from the 70s and has the old Woolworths logo that was never used with Big W. I think this mower was probably sold in select Woolworths department stores, the ones with the concertina wooden framed doors that so many had. I always saw that as their signature feature.
Hello
Gadge and
MowerfreakThere is clear evidence that Big W appeared here, on these shores, in ...
1964.
https://en.wikipedia.org/wiki/Big_WI think Gadge has the clear argument here.
Woolworths may be the fresh gambling and food people ... but lawnmowers?

This takes nothing away from a marketing possibility - that Mowerfreak raises.
I would love image evidence here - to correct, or better understand, this company.
Hope this helps.---------------------------------
Jack