You have a claim in breach of contract and breach of the sale and supply of goods and services legislation against the airline. The Defendant was under a duty in contract law and statute to provide you with a product and service that was fit for purpose, of reasonably satisfactory quality and matched the description at the point of sale. Your damages will be a refund on the purchase price, plus additional costs of rectifying their defective work through another supplier.
You should send a letter of claim to them. There are plenty of free templates online and the consumer protection advice magazine/website “Which?” has a useful template which you can adapt to your claim: https://www.which.co.uk/consumer-rights/letter/letter-before-small-claims-court-claim.
If they do not reply with their reasons for disputing the claim within 21 days, you should issue court proceedings via the Government’s Small Claims Track Online System: https://www.gov.uk/make-money-claim. The issue fee depends on the total damages being claimed. If you issue online, the court issue fee ranges from between £35.00 for a claim worth up to £300.00 damages, up to £455.00 for a claim worth between £5,000.00 and £10,000.00 damages. The Small Claims Court Online Portal will advise you on the fee when you come to issue your claim, but you may check the Government’s Court Fee advice booklet EX50 at PDF page 5/21 accessible at the following link: https://www.gov.uk/government/publications/fees-in-the-civil-and-family-courts-main-fees-ex50.
A party cannot normally recover solicitors’ costs on the Small Claims Track. However, it is designed for non-lawyers (known as “Litigants In Person”). The trials are relatively informal, and the judges do not expect parties to have the same legal knowledge as experienced solicitors and barristers.