I assume you have checked your current by-laws, which are silent about the laundry? The next place to look is on the strata plan. For a 60’s building, it will probably just show the communal laundry as “common property” (“CP” usually). If it references the room as being a laundry then that would possibly make things more complex.
But, the OC has been providing the building with a communal laundry as part of the common property, and so s.106 does require the OC to maintain this, and keep it functioning. If the OC wants to cease providing laundry services, then s.106(3) applies, and the OC can by special resolution (ie roughly 75% support – but actually more complicated), determine that “(a) it is inappropriate the maintain, renew, replace or repair the property, and (b) its decision will not affect the safety of (anything) or detract from the appearance of any property”.
So you hold a general meeting (AGM or extraordinary) with an agenda item to cease providing any laundry services and to close the laundry (or better convert it to another purpose). If that is supported, and not more than 25% of owners don’t vote against it, then that is done.
However, the Building Code might require buildings like yours to provide a laundry or clothes line etc? Your development application might also require this (but building’s from the 60’s typically have a 1-page DA, but you should check that too.) Some one else might be able to respond to whether laundries or clothes lines are required, in building’s where the Units don’t have internal laundries?
Another complication, is that you cannot discriminate and all owners must have equal access to facilities. Getting rid of the communal washing machine is possible, and you can offer the owners use of the laundry room to install their own machines, which are connected to their own lot’s power supply and to the water supply. But you must allow for 8 washing machines, and provide each Unit with its own space there. If you have another room that can be converted to a laundry that will hold the 2nd set of machines, then that could be designated for that purpose, whether or not it is ever used.
You could create a by-law setting out the rules for the laundry; that any owner can apply to locate a washing machine in the specified areas, and the OC will permit this, provided they arrange a power supply to their own lot’s electricity meter, and a connection to the cold water supply. The by-law can specify rules, about times of use, hanging or drying clothes, the type or size of permitted machines, whether driers (or combined washer/driers) are permitted, which will depend on ventilation and fire safety – etc.
Your current room allows for 4 machines, so when the 5th owner applies, the OC will then probably need to convert another room for them to use. Maybe there wont be much demand, if Units have their own laundries. Your laundry by-law could state that the communal laundry room is only available to lots which do not otherwise provide laundry facilities. This could potentially invalidate the by-law by being “harsh, unconscionable or oppressive” (sections 139, 150), so it may be a good idea to have a strata lawyer draft the by-law to minimise that risk.