There's no fixed period of notice between employers and employees. The notice period is defined by the contract that exists between the employer and employee. Irrespective of anything was ever put down on paper, a contract of employment does exist between you and your employee. If you failed to provide your employee with a written 'statement of employment particulars', relating to that contract, (which could have included details of any notice period) within two months of her commencing employment with you, you've broken the law. So you can hardly complain when the employee decides to determine her own interpretation of the terms of the contract which exists between you.
In practice, even when an employee has a notice period defined within their statement of employment particulars, there's little you can do to prevent them simply walking out.. You could theoretically sue them for any loss which you suffer because of their unexpected absence but, in many cases, this would be too time-consuming or impractical.
Chris