I would advise thus...
Speak directly to the owner of club/school first thing Monday morning and appraise him/her of the situation. Have the CAA letter to hand. Politely make your point that you expect the club/school to meet all the costs of the retake and reapplication, whatever they may be. Be polite but forceful...do not accept any negotation or waffle. When the postion is agreed, get it in writing on company paper.
If the outfit is decent there will be no dispute...just embarrassment (on their part) an apology, and a sincere desire to put things right.
And, if the outfit is found wanting, just point out the readers of Pprune will enjoy reading the details.
As you are in England the small claims court will easily recover any costs they do not make good.