It depends on the reason for the termination. If the reason is for 'gross misconduct' the law may allow dismissal without notice, that is, a 'summary dismissal'. Even where you are dismissed for gross misconduct you may have a claim for unfair dismissal, particularly if there is no proper investigation and disciplinary hearing. Otherwise failure to give notice could entitle you to bring a claim for breach of contract in an employment tribunal or a civil court.
Claims to a tribunal for breach of contract, on termination of employment, do not require any qualifying service. This type of claim is known as one for wrongful dismissal. Also, where you are dismissed just before you were about to acquire sufficient service (as of 6 April 2012, two years) to bring an unfair dismissal claim all may not be lost. Specifically, a tribunal has the power to extend service by up to a week.
