Hello my name is ***** ***** I am happy to help you today, do you have any reason to suspect your termination amounted to discrimination or that you were dismissed for lodging a health and safety complaint?
Ok in that case unfortunately there is no claim that can be brought. UK employment law does not protect people who have less than 2 years service unless they are discriminated against contrary to the Equality Act, it is one of the fundamental weaknesses of employment law in this country.
Wrongful dismissal is a failure to pay notice. If you have been given correct notice then there is no claim for wrongful dismissal.
You should also have been paid in lieu of outstanding holiday. If you have not then there is a claim for breach of the Working Time Regulations.
Yes, if you are aware there is an overpayment then you are legally obliged to repay it. Your employer should be reasonable in the terms for repayment. i.e. it should let you repay over a period if you cannot repay it all at once.