Can I get visas to travel from Vietnam to the UK and go to Australia and then go back to Vietnam?

Based upon what you wrote, you will need two visas. You will need to apply for the UK visa before leaving. Ideally both, you can ask for the Aussie visa to be post dated 3 months forward and that will give you enough time. Applying for the Aussie visa from in the UK will be awkward without a compelling reason since you knew you would be applying before you left, and expect them to enquire about that. Also it could be awkward unless you bring all the documentation they need with you, and you'll be without a travel document in the UK while the application is pending (which is never a great idea). Flight information from Viet Nam can be handled by an internet search.

It's possible for you to visit UK and Australia as long as you have a valid Visa. You must apply a travel Visa to UK and tourist Visa to Australia. Vietnam is not an ETA-eligible country to apply an ETA visa to Australia so I suggest you to apply for a Visitor Visa instead.