I dunno we could try something radical like actually making asylum decisions? Then either they'll be granted status to remain in the UK and have the possibility to start working and earning a living in the UK or, if their claim fails we should swiftly deport them (pending the outcome of any appeals, which should also be resolved promptly).
Might also not be a bad idea to think about ways we can make use of the more skilled asylum seekers who are successful in their claims to put their skills to use. We need more doctors and nurses in the NHS, so we should be leaning into schemes like the British Medical Associations refugee doctors initiative:
The steps you can take to get a job as a doctor in the UK, more about our refugee doctor initiative and help with GMC registration.
www.bma.org.uk
I imagine there's other refugees that live in the UK with in demand skills who cannot use them due to problems with evidencing their competence and the lack of cross-acceptance of previous awarded certificates.
Good job that the number of asylum claims is only about 60,000 a year. Not sure that 60,000 extra people a year is really going to make that much of a difference in a country of 67 odd million. Quite apart from the fact that we've always managed to integrate, often far more successfully than elsewhere, newcomers to this country. It's something we're actually quite good at.
As for the crime aspect this is obviously more complex but it is worth noting that crime in general has continued to fall over the long term (even if it does get more play in the media that it used to) and also that I rather suspect that the rates of crime between asylum seekers/refugees and the UK born population are not all that different. Particularly if you compare them with those UK born citizens who live in deprived areas. A lot of crime has far more to do with poverty and lack of opportunity than whether you were born in the UK or not.