Costs
13.—(1) An adjudicator must not normally make an order awarding costs and expenses.
(2) But, subject to sub-paragraph (3), an adjudicator may make an order awarding costs and expenses—
(a)against a party (including an appellant who has withdrawn an appeal or an enforcement authority which has consented to an appeal being allowed), if the adjudicator considers that—
(i)the party has acted frivolously or vexatiously, or
(ii)the party’s conduct in making, pursuing or resisting an appeal was wholly unreasonable;
(b)against an enforcement authority, where the adjudicator considers that the disputed decision was wholly unreasonable.
(3) An order must not be made against a party unless that party has been given an opportunity to make representations against the making of the order.
(4) An order must require the party against whom it is made to pay to the other party a specified sum in respect of the costs and expenses incurred by that other party in connection with the proceedings.
So the answer to your question is yes, costs may be awarded. But these are exceptional. Do the facts of your case - the factual and procedural not just whether your appeal was allowed- meet the threshold test for costs?
Post your case number(if London) and we can have a look.