What happens if the employer does not give me notice of termination of employment to end my contract?

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', (although 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 tribunal for breach of contract, on termination of employment, do not require any qualifying service. A tribunal has the power to extend service by a period equivalent to notice.