A lot of your post isn't making sense to me in the premise of it, leading to the strange questions you're asking.
I've realised that most of the public chargers (at least in Australia) out there have type 2 ports.
Right. Australia uses the Type2 plugs on the public charging stations and the charging ports in the cars, just like Europe does.
I was wondering if there's some sort of adaptor which is available, which can go into the end of the UMC cable and have the plug as type 2?
This is the part that doesn't make any sense. The UMC cable should ALREADY have a Type2 plug on it. The UMC cables that are sold to go with the cars in Europe and Australia are made with the Type2 plug on the UMC. I'm not sure what kind of "adaptor" you mean, because there's nothing to "adapt".
so I wouldn't have to 1 spend a lot of money on the type 2 to type 2 cables (assuming the adaptor would be cheaper) and 2 it would just be less cables to carry, as I'm already carrying the UMC kit.
But then this shows a misunderstanding of what the pieces of equipment are. There is a device called an EVSE (electric vehicle supply equipment). That does the communication with the car, announces how many amps are available and negotiates it with the car, does some safety checks, and then closes a switch. You use only exactly ONE of those in your connection path. The UMC is one of those devices. That little box in the middle has the electronics in it that is the EVSE.
That UMC is used ONLY for plugging into regular electrical outlets. At a public charging station, the EVSE electronics are already inside the station. The Type2 to Type2 cable is simply a wire. You can't use the UMC to plug into those charging stations, because that would be trying to plug one EVSE device into another EVSE device, and you don't chain them like that.
So yeah, you need to just get a Type2 to Type2 cable.
Or preferably for much faster charging, you might want to check for fast charging stations that have the CCS2 plug handle. Those will plug directly into the car's charge port.
We use the app or website called Plugshare, which shows all kinds of charging resources, and you can filter by plug type. I'm not sure how well Plugshare covers Australia, or if there is a better alternative there. You might check the Australia regional section of this forum with that question.