I have heard so many implausible explanation for why Australians call Brits "Poms". But they do and it is ubiquitous. The most ludicrous is a reference to Pomegranates: ie pasty Brits arrive in Australia and after two days in the sun look like the inside of a Pomegranate. Totally implausible!
Here is my explanation gleaned from a BBC programme on Prison Reform.
The convicts waiting for deportation were kept in Millbank Prison on the river in London. Millbank is still there next to Tate Britain and once the home of the British Labour Party, but the prison is long gone. Each Prisoner wore a uniform with ‘Prisoner of Millbank’ stamped on the back which became abbreviated to P O M.
When the ships rolled into Botany Bay the prisoners still had their uniforms and so the local population would remark: ‘here come more POMs’. And it stuck.
That sounds plausible doesn’t it?