Show Me The Money
If you have not been dismissed for gross misconduct and you have not received the correct amount as a payment in lieu of notice then you can bring an employment law claim to the Employment Tribunal or the Court for the amount due to you. You should also note that you are unlikely to be bound by an post termination restrictions. In English employment law you would be under a duty to ‘mitigate your loss' - this simply means you are required to try to find another job. If you were to get another job during the notice period the compensation you would get would be the salary you lost from the date of your wrongful dismissal to the date of commencing your new job. In practical terms, this means that were a senior city executive is being dismissed and they have a long notice period, delicate negotiations are necessary to find the balance between the employer having to pay the full notice period and the likelihood of the senior high flyer finding a new job. To put this in context, Sir Iain Blair, got paid out his full contract - presumably as no-one could see him getting a new job. By contrast, most football managers get a proportion of the amount left on their contract.
Finally, you should remember it is possible to have a claim for wrongful dismissal and a claim for unfair dismissal and a claim for constructive dismissal.