Unless you are under the age of 18, a 3 year time limit applies. That is, you must bring your claim and ensure certain things have occurred within 3 years of the date of the accident.
The relevant legislation requires you to lodge a Notice of Accident Claim Form within 1 month of consulting a lawyer about bringing a claim. Because it is a hit and run case, you should involve the Police immediately and deliver the Notice of Accident Claim Form to the Nominal Defendant within 3 months of the accident. If the Notice of Claim is not given to the Nominal Defendant within 9 months of the accident, the claim is barred.