Would a properly functioning asylum system...

...ie one where claims were quickly and fairly processed and heard; and those whose claims were dismissed were promptly removed...   

If this were made to happen in the UK, might it actually increase the number of people making asylum claims?   

Let's leave aside the costs that might be involved, or practicalities such as removing people to countries of origin that might not want them back.  

Depends on the criteria.  If it only allows 10% of claims and has people on a flight home within a week it’s probably a deterrent but if it allows 80% claims then it probably acts as a draw for claimants.

Indeed but it would reach an average based on the given parameters and that average could be a deterrent or an encouragement.

No it would fluctuate over time based on world events and how many legit asylum seekers are floating about vs illegit. 

Process fast and deport those who don't make the criteria. And those who do make it, their right to remain is only for so long as the circs of asylum remain (i.e. regime change, and they go home). 

And those who do make it, their right to remain is only for so long as the circs of asylum remain

What if they become productive members of their community, doing valuable jobs, contributing to the exchequer and they want to stay?

The percentage of asylum seekers recognised as refugees varies very significantly among different European countries, even when adjusting for countries of origin of the asylum seekers.  There is no supra-national court of authority aligning interpetation or application of the rules.

About 2 bn people on the planet are likely eligible by "the criteria" as they're generally understood (probably more if you count places that are generally safe but dangerous for specific groups).

I don't understand why so many middle class people pretend not to realise this.

Process fast and deport those who don't make the criteria.

How are you going to efficiently deport people who don’t have travel documents, a necessary requirement for countries of origin to take them back? That’s where reality tends to bite on this stuff.