There are two types of notice – statutory and contractual. You will be entitled to insist on whichever is longer.
The law states that you are entitled to at least one week's notice if you have worked for your employer for anywhere between one month and two years. After that you are entitled to one week's further notice for every year of service up to 12 years' service. So for six years' service you would be entitled to six weeks' statutory notice and for 20 years' service you would be entitled to 12 weeks' statutory notice.
These statutory notice periods are minimum notice periods and a contract of employment may give you a longer entitlement. A month is a common contractual notice period – which may or may not be longer than your statutory notice period.
In cases of redundancy, there must be at least one consultation meeting before a final decision is taken and the formal notice of termination of employment is given. The consultation period can be used, for example, to see whether an alternative to redundancy is possible.
Even where an employer believes that serious misconduct has occurred, the employer must still act fairly and reasonably by conducting a proper investigation and giving the employee a proper opportunity to explain their version of events or to challenge the allegations, and must follow the employer's own disciplinary procedures. It must also comply with the requirements of the Acas Code of Practice on Disciplinary and Grievance Procedures (PDF, 167KB).