“Not often” is the answer. Only if the tribunal acts in an improper way. Incompetence or unlawfulness is not sufficient.
In this case, R (on the application of Gudanaviciene) v Immigration and Asylum First Tier Tribunal  EWCA Civ 352, an EU national was facing deportation. She appealed the decision to deport but no legal aid was available to assist her and she could not afford to pay for legal representation. A good firm of solicitors, Turpin Miller in Oxford, agreed to take on her case but only to the extent that they would, unfunded, help her apply to the Legal Aid Agency for “Exceptional Case Funding”.
Her application for legal aid was ultimately successful, although not before her case became the test case on the circumstances in which exceptional funding might be granted. See R (on the application of Gudanaviciene & Ors) v The Director of Legal Aid Casework & Or  EWCA Civ 1622.
While the application for legal aid was still being resolved, what happened to the appeal for which the legal aid was needed? The solicitors applied for an adjournment of the appeal so that the application for legal aid could be decided. After all, what would be the point in applying for legal aid at all if the appeal for which the legal aid was needed was decided first?
Any reasonable person would expect such an adjournment application to succeed. But no. The adjournment application was refused:
The Resident Judge indicates that the Tribunal is not concerned with funding.
The resident judge is understood by the Court of Appeal to have been Judge Renton at that time, who has subsequently retired.
There was a certain amount of toing and froing, with the solicitors repeatedly making representations on the need for an adjournment – all at their own expense. It must have rankled, then, when a further refusal of the adjournment stated:
The Resident Judge indicates that the decision of the 6th December 2013 is repeated. The issue is one of funding and the appellant is legally represented.
The appellant was represented in the judicial review proceedings, not in the appeal. That was what the judicial review was all about.
Accessible and practical guide to costs in appeals and judicial reviews including rules, guidance, case law, quantification and assessmentView Now
In the face of this refusal to adjourn and the risk that the (ultimately successful) judicial review of the refusal of legal aid would be rendered pointless, the solicitors then applied for judicial review of Judge Renton’s refusal to adjourn. Judicial review was the only option as there a no right of appeal against refusal of an adjournment. Relief swiftly was granted by Jay J, who ordered that the appeal should not take place until after the final decision on legal aid funding for that appeal.
Finally, the tribunal appeal was adjourned.
The solicitors had done considerable unfunded work to secure this result, and the application for judicial review of the tribunal’s adjournment decision had succeeded. Normally, the successful party will recover his or her costs from the loser, who in this case would be the immigration tribunal. Submissions were made on costs but no order for costs was made, leaving the solicitors considerably out of pocket despite their client having succeeded. That costs decision was appealed to the Court of Appeal.
In the meantime, the successs of the judicial review against the refusal of legal aid enabled her to be legally represented. The appeal eventually went ahead and Ms Gudanaviciene’s appeal against deportation succeeded, despite an appeal by the Secretary of State to the Upper Tribunal.
You really cannot fault the solicitors for their capacity to undertake litigation. However, the appeal to the Court of Appeal was unsuccessful, despite the Court recording their opinion that Turpin Miller had provided “sterling service” to their client.
The problem for the solicitors was the case of R (Davies) v Birmingham Deputy Coroner  EWCA Civ 207 in which had been held that an order for costs should only be made in favour of a successful claimant against an inferior tribunal if the tribunal appeared in court otherwise than in a neutral way or there had been a “flagrant instance of improper behaviour”:
(1) the established practice of the courts was to make no order for costs against an inferior court or tribunal which did not appear before it except when there was a flagrant instance of improper behaviour or when the inferior court or tribunal unreasonably declined or neglected to sign a consent order disposing of the proceedings; (2) the established practice of the courts was to treat an inferior court or tribunal which resisted an application actively by way of argument in such a way that it made itself an active party to the litigation, as if it was such a party, so that in the normal course of things costs would follow the event; (3) if, however, an inferior court or tribunal appeared in the proceedings in order to assist the court neutrally on questions of jurisdiction, procedure, specialist case law and such like, the established practice of the courts was to treat it as a neutral party, so that it would not make an order for costs in its favour or an order for costs against it whatever the outcome of the application; (4) there are, however, a number of important considerations which might tend to make the courts exercise their discretion in a different way today in cases in category (3) above, so that a successful applicant, like Mr Touche, who has to finance his own litigation without external funding, may be fairly compensated out of a source of public funds and not be put to irrecoverable expense in asserting his rights after a coroner, or other inferior tribunal, has gone wrong in law, and [where] there is no other very obvious candidate available to pay his costs.
This authority was considered to be applicable, the FTT had not made any appearance before the Administrative Court to attempt to defend its decision and there was apparently nothing flagrantly improper or partisan about the tribunal decision. The correct order was therefore no order for costs.
Some of the reasoning is… interesting. Longmore LJ considered it relevant to the question of recovering costs that the only reason the judicial review had been brought was because there was no right of appeal. Further, to make an award of costs against the tribunal would offend against the principle of judicial immunity, which was a particular concern where there was apparently no statutory provision indemnifying members of the First-tier Tribunal
all of whom … might therefore be exposed to an unimdemnified personal liability.
Heaven’s forfend. Someone ends up paying the cost of Judge Renton’s unreasonable decision. Rather it be the lawyers than it be the judge, the Court of Appeal concludes.