I am referring to the UK Human rights law too, as listed below - so even if a person HAS had all their checks done, our Human rights law specifically states that The UK cannot deny basic housing to an asylum applicant if doing so would lead to destitution or a breach of human rights, regardless of their past.
there is also the problem of data sharing, if an asylum seeker committed a crime in their home country (e.g., Iran, Syria, or Eritrea), it is often found that many nation's governments do not share its criminal records database with UK authorities and so we have no idea, until after a crime is committed here.
also, if a person arrives in the UK without a passport or identity documents, the initial biometric checks can only flag them if they have previously interacted with law enforcement in the UK or Interpol. A clean database result simply means the UK has no existing record of them, not that they have never committed a crime abroad.
so in summary, the checks aren't as stringent as you may think.