I had a matter to deal with in the disputes tribunal. The…

You can try an appeal but the problem is the jurisdiction of the Tribunal is such that appeal rights are very limited. The act says, at Section 50

50Appeals

(1)

Any party to proceedings before a Tribunal may appeal to a District Court against an order made by the Tribunal under section 18(8) or section 46(2) or section 47(3)(b), or against the approval by the Tribunal of an agreed settlement under section 18(3), or against the variation of a term of an agreed settlement under section 47(3)(a), on the grounds that—

(a) the proceedings were conducted by the Referee; or

(b) an inquiry was carried out by an Investigator—

in a manner that was unfair to the appellant and prejudicially affected the result of the proceedings.

(2) Without limiting the generality of subsection (1), a Referee shall be deemed to have conducted the proceedings in a manner that was unfair to the appellant and prejudicially affected the result if—

(a) the Referee fails to have regard to any provision of any enactment that is brought to the attention of the Referee at the hearing; and

(b) as a result of that failure, the result of the proceedings is unfair to the appellant.

(3) An appeal shall be brought by a party by the filing of a notice of appeal, in the prescribed form, in the District Court of which the Tribunal is a division, within 28 days of the making or giving of the order or approval or variation appealed against, or within such further time as a District Court Judge may, on application, allow.

If you can persuade a District Court judge that the result was unfair they will direct a rehearing. But generally issues of fact are not easy.