The ACAS website contains very helpful advice on this topic (as on so much else). However, the key thing is that employers should not only have documented policies in place but actually follow them.
An analysis of successful claims before the Employment Tribunal will show that a preponderance of such claims have depended on the employer making procedural errors in their handling of disciplinary matters leading to a conclusion that their treatment of the employee was unfair.
Normally an employee is not able to bring an unfair dismissal or redundancy claim unless they have been employed for a continuous period of 2 years. But there are exceptions and discrimination claims can be brought at any time during employment.
Again, whether you are an employee concerned about what is happening in your place of business or an employer trying to do the right thing on behalf of their business, it makes sense to get advice.