On what grounds? Unfortunately I do not believe there is much you can do. You appear to have been paid in lieu of notice and there is no obligation on an employer to employ someone. Until you have one year's continuous employment, you cannot claim unfair dismissal and although there are exceptions under which unfair dismissal with less than one year's service, you don't from the information given appear to fit one of these groups. They are dismissals related to trade union membership, to pregnancy, childbirth or maternity, for health and safety reasons, dismissals related to part-time status or dismissals related to enforcing the right to be paid the minimum wage.