If you are employed for one month or more you are entitled to a week of notice. Whatever probationary period the contract stipulates I do not see how it can override this.
The OP states that she has only been employed for 3 weeks so the statutory requirement do not apply. Although it is not clear whether the company is paying her the notice as many pay monthy and she would most likely recieve a months salary with one week being in lieu of notice. Although they are not required to give any.
My reply was poorly worded I'll grant you.
An employee cannot claim unfair dismissal in the first year of continuous service, unless they have been discriminated against unlawfully, they can then lodge an Employment Tribunal at any time.
In law, the employer must ensure that the employee
1: Is given the correct training and support
2: Understands what is expected within the job role
3: Understands the areas in which he/she is underperforming
4: is given sufficent time to improve
They must be issued with warnings as per the companies disciplinary procedures and given the relevent rights to notice and representation.
Unfortunately as she was dissmissed before she completed a full months service the employer is not required to give notice or follow any of the above requirements.
Where there is no discrimination, an employee can have his/her employment terminated
unfairly (eg. You dont fit in or some such rubbish) at any time with the first 12 months as long as you follow any contractual disciplinary procedures (normally the statutory 3 stage dismissal procedure) and give the required statutory notice.
Probationary periods simply allow the company to monitor and appraise an employee during the initial stage of their employment.