If your training has been called an 'apprenticeship', and your employer has been paying you at the rate of pay (lower than the usual National Minimum Wage) which applies to apprentices, the scheme MUST lead to a formal qualification, as stated here:
http://www.apprentice...ntice/The-Basics.aspx
If you've only been receiving 'apprentices' pay, and there is no such qualification available, your employer owes you all of the money which you've missed out on by not receiving the normal National Minimum Wage. (i.e. you were never legally an 'apprentice' and the employee had no right to pay you at the lower rate).
If you've not entered into a formal apprenticeship (and you've been paid in accordance with the National Minimum Wage for a 'non-apprentice') then any training system has been entirely informal and the salon is free to decide whether they'll award their own certificates to anyone.
Chris