Perhaps because the UK and Ireland have a Common Travel Area? You don't need a passport to enter the Republic, any more than Yorkshire. (In reality, you may be asked for an ID like a driving licence, but I doubt that is needed on the island of Ireland, once you've got there.) Now, I don't know the full SP of the CTA, but it looks like undesirables can legally be sent back. Presumably, this works both ways.
We don't have a common travel area with the rest of the EU and Brexit meant we gave up the Dublin Agreement. So, we have no agreed system to return these people to France.
As for the Australian immigration system, it's what we have, more or less. To get a visa to immigrate, you have to hit a points target. Same as Australia. On the basis of the latest data I have seen, 97% of total immigrants have a visa given to them by the UK government. Mostly, I presume, for economic reasons.
All Brexit did was reduce EU immigration and replace it with Commonwealth and Third World immigration. And increase the total numbers. People coming from further away, without free movement, are all the more likely to stay here permanently. Many EU immigrants stayed for a bit, then went home to Poland or wherever.