To Australian low income workers who have also worked on the minimum wage in the UK also?

I have a debate with my Australian friend that living on the minimum wage in the UK is worse than Australia. As a single person with no dependants our minimum wage is £6.50 per hour gross which is $12.35. On a 40 hour week and with rent to pay can you tell me if you get your wage or/and rent topped up by the government if let's say you are only on a 16 hour week or don't make enough money for food and rent? I know cost of living is high in both countries..food more pricey but rent in general is cheaper in Oz. She says there are 4 bands in Oz for pay rates also. Can somebody enlighten me please.