Can a person currently, under British HSMP, apply for Australian immigration?
If you mean can you apply within the UK for an Australian immigration visa, since you are resident in the UK, the answer is yes. Anyone can apply for an Australian immigration visa in their country of residence or citizenship. Your HSMP will hold no merit in the process, apart from showing that you are a law-abiding foreign resident. This UK visa will not necessarily make the process easier than it would be in your home country.