Anonamous letters sent to employer taking the character of

Thanks for your patience. It is actually not unlawful for an employee to use anonymous information to take disciplinary action against an employee. Generally they would need to complete a reasonable investigation and show they had a genuine belief in the allegations against the employee but in this case the employee’s service will go against them.
If you have been continuously employed at your place of work for less than 2 years then your employment rights will unfortunately be somewhat limited. Most importantly, you will not be protected against unfair dismissal. This means that your employer can dismiss you for more or less any reason, and without following a fair procedure, as long as their decision is not based on discriminatory grounds (i.e. because of gender, race, religion, age, a disability, sexual orientation, etc.) or because you were trying to assert any of your statutory rights (e.g. requesting maternity/paternity leave, etc.). In the event that the reason for dismissal fell within these categories, then the dismissal will either be automatically unfair, or there will be a potential discrimination claim.
If the dismissal had nothing to do with any of the above exceptions then you would not be able to challenge it and your only protection would be if you were not paid your contractual notice period, because unless you were dismissed for gross misconduct, you would be entitled to receive your contractual notice period. If you did not have a written contract in place you would be entitled to the minimum statutory notice period of 1 week. Your employer would either have to allow you to work that notice period and pay you as normal, or they will have to pay you in lieu of notice.
If you were not paid your notice period when you were due one, that would amount to wrongful dismissal (which is different to unfair dismissal) and you could make a claim in an employment tribunal to recover the pay for the notice period that you should have been given. There is a 3-month time limit from the date of dismissal to submit the claim.
So they can take disciplinary action and even dismiss for no apparent reason, without any evidence and even if based on anonymous evidence.
I hope this has answered your query. Please take a second to leave a positive rating, or if you need me to clarify anything before you go - please get back to me and I will assist further as best as I can. Thank you