There is no legal requirement to pay a higher rate for overtime than for for normal working hours. As long as hourly rate meets the requirements of the National Minimum Wage (currently �5.35 per hour for employees aged 22 and over) the law is satisfied. (In my last job, within the rail industry, it was standard practice that staff received the same rate for all hours worked, whether or not overtime was involved. Up until recently, junior hospital doctors only received one third of their normal pay rate while working overtime i.e. their pay was much
lower than normal during overtime).
Public holidays have no special status within employment law. If a public holiday falls on a day when an employee would normally be at work, the employer has the right to expect the employee to work at their normal pay rate. (When I worked on the railways, public holidays were always worked at the usual pay rate. I've previously done bar work, on Christmas Day, at the regular pay rate).
All employees have a contract with their employer. This automatically comes into existence as soon as the employee accepts the job offer. However, employers are also obliged to provide employees with a written 'statement of employment particulars' within two months of the commencement of the employment.
Full information about employment rights (together with guidance upon appropriate action if these rights are breached) can be found here:
http://www.direct.gov.uk/en/Employment/Employe es/index.htm
Chris