Personal injury cases can take some time to settle even when liabiility has been admitted by the third party.
If it is settled too quickly, the there is a very good chance that your claim has been undervalued.
As a very rough rule of thumb, minor to moderate injury claims settle in 12 - 18 months. Moderate to severe will settle between 18 - 36 months and catastrophic can be 5 years +
Bear in mind that proceedings have to be issued within 3 years of the date of injury or the date of knowledge, whichever is the sooner otherwise the case becomes time barred (except under certain circumstances), and if the other side accept liability, they may still try and attribute some contributory neglligence which will and can delay things even further
