Where notice to abandon an appeal has been duly given by the appellant—
(a) the court against whose decision the appeal was brought may issue process for enforcing that decision, subject to anything already suffered or done under it by the appellant; and
(b) the said court may, on the application of the other party to the appeal, order the appellant to pay to that party such costs as appear to the court to be just and reasonable in respect of expenses properly incurred by that party in connection with the appeal before notice of the abandonment was given to that party.
In this section "appeal" means an appeal from a magistrates' court to the Crown Court, and the reference to a notice to abandon an appeal is a reference to a notice shown to the satisfaction of the magistrates' court to have been given in accordance with rules of court .