Conduct (or more accurately, 'misconduct') is one of the potentially fair reasons for dismissal, so accusations of misconduct should not be ignored. You need to ask your employer to set out in writing exactly what the accusations against you are.
Certain types of misconduct are classed as 'gross misconduct'. If, following a proper disciplinary procedure, you are found to be guilty of an act of gross misconduct, your employer will be entitled to dismiss you without any notice or payment in lieu of notice.
Proven accusations of less serious misconduct might result in some type of formal warning. Your employer should have a disciplinary code which sets out the penalties that can be applied. All employers must have a disciplinary policy in place, which should set out the likely sanctions for different levels of misconduct, for example a First or a Final Warning.
For any process to be fair, you need to know exactly what you are accused of. Your employer must give you enough advance notice of the charges against you, and the evidence relied on to support those charges, to enable you to prepare properly, so that you can put your side of the story.
The rules you are accused of breaking need to have been clearly set out, usually in a disciplinary procedure. They must also have been clearly communicated to you before the date of the alleged misconduct, for example by making the procedure available to you in a hard copy, or on your employer’s intranet, and/or by drawing the rules to your attention through induction or training.
If you believe you are not guilty as accused, you need to gather together evidence to demonstrate that you have not committed the act of misconduct. If you believe you might be guilty, you need to gather as much evidence as possible that will help to mitigate or reduce the implications of being found to have committed the act.
Consult your organisation's disciplinary procedure to see what process might take place and to see if it outlines examples of misconduct and whether the one you are accused of is listed. (If your organisation only has a basic disciplinary procedure, consult the Acas Code of Practice on Discipline and Grievance Procedures (PDF, 167KB).
If you are a member of a trade union, discuss the matter with your union representative at the earliest opportunity. Even if your employer does not recognise a union, if you are a union member you have the right to be accompanied by your trade union rep at a disciplinary hearing.
If you are not a member of a trade union, you can still approach a trade union for assistance and request that you be accompanied at a disciplinary hearing (although, understandably, most unions will only help existing members). Alternatively, you may identify a work colleague to accompany and assist you.