Right, and I agree with you that, in principle, the fact that there is no easy way to claim asylum in the UK is a problem and that results in terrible suffering that we really should be trying to prevent. But... there must be hundreds of millions of people across the World who are being persecuted and would have very good grounds to claim if they were able to do so. I have yet to see any serious suggestion for how you could reasonably make it easy for people who are being persecuted to claim asylum in the UK that wouldn't be likely to result in our suddenly being faced with, maybe millions of legitimate claims a year - which we could not possibly accommodate (as well as potentially millions more people who don't really have legitimate claims but thought they'd try their luck). That's the dilemma which few of the Government's critics seem to recognise.
Maybe there needs to be a better system which isn't done by country, rather is done with all countries working together.
Anyone anywhere can claim asylum, their case is reviewed (with details like where family/ties exist) and a decision is made at to if they meet the requirements to be given asylum and a recommended country given. There would be agreements in place determining the numbers given access to a given country.
Monitoring would be in place to determine where is likely to create displaced people and the likely numbers.
Support would be given to house people locally to their home (i.e. a neighbouring country), however where possible there should be measures in place to allow them to work so the level of support could be reduced - i.e. they do jobs to improve conditions in the migrant camps they are staying in to reduce the cost of the facilities.
They would be expected to stay there (or some other safe country, if the nearby country was also a risk to them) whilst their application for asylum was processed. The cost of this would likely be significantly cheaper than housing them in the UK or other Western Country - even if the numbers were higher).
Reception countries could provide details of roles/industries where there's a shortage of staff and if people meet those positions the reception country could offer them a place of a suitable job could be found for them (potentially without having to go through the full asylum process). For example, if a doctor was escaping a regime and their English was good, then the UK could offer them access to NHS jobs rather than going through the full asylum process (cuts costs of having to process them as much, and fills a job which otherwise might not be filled for some time).
Yes you could find that you end up with more people who are displaced seeking asylum, however they could end up in any country, so the attractiveness of being sure of getting a Western Country would reduce. Now if it's due to (say) homophobia they're unlikely to end up in (say) an Arabic country, so there would be a certain amount of above average cases heading towards Western Countries for such cases. However they could be balanced by other cases going elsewhere.
There would be some countries who would like to have more people (for instance Canada is fairly keen on having now people living there), whilst others less so.
At least some of the people able to pay the people smugglers to get to the west could well fund some of their own costs (for example travel costs) if needed. To encourage that there could be like a student loan setup which added a "tax" once the individual earned over a certain amount to repay their travel costs. However, with there not being a need to be on a given flight block booking of commercial flights could be done as the bookings opened to get the best value air fare.
Even just at an EU or Commonwealth level there would likely be advantages to both the countries but also the people.