Immediate dismissal will only be justified for the most serious offences - for example, theft, taking bribes, or sexual harassment - which constitute gross misconduct. Once you have concluded the appropriate disciplinary procedure, you can dismiss the employee without notice.
Be careful. The fact that you consider an offence to be gross misconduct does not mean that an Employment Tribunal will agree with you. The Tribunal will decide whether your response falls within the band of reasonable responses open to an employer. If it falls inside the band, it is fair; if it falls outside the band, it is unfair.
