That is totally unprofessional, unethical and illegal.
If a member of staff makes a mistake (like loose £10) they should at least be interviewed after an investigation, and if necessary be issued with a warning. However this seems like a genuine mistake, which with good management should have been treated as just that. In no respect is it gross misconduct that would warrant instant dismissal, and in any case cannot be classes as such due to legally demanded disciplinary procedures obviously not being adhered to.
All communication in respect of a case like this should have been dealt with by a face to face interview, and if required a letter noting the employee's misdemeanor.
The company must have by law issues her with a contract which should itemise the company's disciplinary procedure. On all occasions this must be followed, with failure to do so being classed as unlawful.
This young lady was also entitled to payment in lieu of notice and holiday pay. As her 'instant' dismissal was not legal then she is entitled to these payments.
Inspite of only working for this company for 8 months, she does has legal rights and I would recommend she speaks to a solicitor immediately claiming WRONGFUL and therefore also UNFAIR dismissal.