A cruise from Australia all the way to the UK will not be "inexpensive" unfortunately. It's a long way, and mostly only done as part of a World Cruise. The less expensive companies include Princess, P & O and Holland America. You can search on their websites for cruises.
Solo travellers don't get a good deal generally from cruise companies. Single bed cabins are unusual, so they are putting you in a 2 bed cabin, and they often ask you to pay double for this. If you can be flexible and go on relatively little notice, you may get a better deal as a single traveller. The sweet spot is about 3.5 month before the sailing date, when final payments become due, and people who paid a deposit a long time ago may now have to change their plans and cancel.
You will get a bigger choice if you are prepared to fly either to the east coast or to Singapore and commence the cruise there.
There are several specialist cruise travel agents in Australia, who have good websites where you can see what cruises are available. Clean Cruising and Cruise Guru are two you might look at.