An asylum seeker has a right to one appeal. The appeal must be made within 15 working days of the negative decision. Appeals are made to the International Protection Appeals Tribunal (IPAT). No further right of appeal exists.
If a person wishes to challenge the process of making a decision they can ask the High Court to review a decision. This is called judicial review. This is less a review of the decision and is primarily concerned with the decision-making process.
Delays are due to backlog in our legal system, not because of applicants ‘drawing out’ procedure.