I would endorse ExXB's advice, but add the comment that the so-called "Small Claims Court", aka
"Money Claim Online" is the way to go.
You file on line, present your case in simple laymen's terms clearly and succintly. You attach the evidence that substantiates your case; ie documentation about the flight, your ticket, evidence of the delay and finally evidence from the CAA (See PS). You do not need to get a lawyer to do that; legal expertise is not required from the claimant. The Judge provides that.
The case will be considered by a Judge; you do not have to attend, and ExXB is right, on what you say you should win.
The filing fee goes up from £25 with the claim value. It's not a lot. You can claim reimbursement of reasonable expenses, legal compensation due, and the filing fee. Don't bother with spurious claims about your time, punitive payments etc etc.
The fee is an excellent investment.
Edit: PS I should have added that a reference and maybe short description of the law about compensation under which you are claiming would be a good idea.