Ms Jones (pictured), who met recently with members of Llangollen Refugee Support Network, expressed particular reservations about how survivors of torture are sometimes turned away on "specious grounds".
The MP referred to a report authored by the organisation Freedom from Torture that documented how asylum caseworkers without any clinical qualifications often replace the expert opinion of a medical doctor with their own speculation about clinical matters.
She said: "The current set-up contravenes a clear Home Office policy on how to handle expert medical evidence of torture.
"Too many Home Office decisions with medical evidence of torture are poor and have to be corrected by judges. This is wrong in principle and it is also wrong in that it is a waste of taxpayers' money."
Ms Jones also expressed her opposition to an Official State Visit to the UK by new US President Donald Trump until his "discriminatory travel ban" has come to an end.