Many close companies or family companies do not have contracts of employment with the Directors.
A contract is not so necessary if the role is just Advisory and you take mainly dividends rather than a fixed salary through PAYE. Some companies do not make enough profit to pay salaries to Directors - at least in early stages, so a contract may not be so relevant.
Contracts of employment are useful because they provide certain rights like ability to claim redundancy, arrears of salary, holiday pay or other statutory entitlements should the business become insolvent. Often Directors assume that 'implied' terms or verbal contracts are sufficient but the terms written down within a contract remove any doubt about the status as an employee and terms in case of disagreement or insolvency.
The main terms set out in a contract should include: hours of work; rate of pay (minimum wage at least); holidays and holiday pay entitlement; grievance and disciplinary procedure; the directors duties and responsibilities; date of commencement; arrangements as to sick leave and sick pay. ACAS is a useful source of free information.