Can anyone suggest who could do this? I haven't much stuff to take, just a few personal items with a number of small and medium boxes. Any help much appreciated....

When I have need to send a few things, say 6-16 boxes of relatively heavy things, I have used a "freight forwarder", for example when I eventually cleared out all my stuff from my parents' loft, and later the tools and things that my father left me, (which were of no use to my mother).

To find a freight fowarder, Google <"Your town", UK, Freight forwarder> (without the < > ).

Look for a company that provides retail service (not all do), and also one that does pick up from your location, assuming that is important to you.

The company you chose will take your boxes, complete the necessary paperwork, and then arrange for shipment by sea or air* to Australia, where an agent will deal with the import paperwork, and either make your stuff available for collection, or to have it delivered to an address per your instructions.

* The last time I sent somethings from the UK to the US I was told that for small quanitities (volumes) there was no cost saving in sending something by ship even if it was something heavy such as boxes of tools, and they recommended air shipment.

thank you

Seven Seas have a good reputation for UK to Aus and vice versa. Worth asking them for a quote.