A few points:
1. You've always had a contract of employment, even if nothing was ever written down. (A contract automatically exists between an employer and an employee).
2. You're employer was obliged to provide you with a 'written statement of employment particulars' within two months of you starting work, so you're employer seems to have been breaking the law.
3. Since 1st April 2009, ALL employees have been legally entitled to 5.6 times the number of days worked per week as their minimum holiday entitlement (subject to a cap of 28 days, so those who work 6 days per week only get the same holiday entitlement as people who work 5 days per week). It needs to be remembered though that all 'enforced holidays', when (for example) the firm is closed for business [such as Christmas Day and other public holidays, if appropriate] are included within that entitlement.
4. With exception of people who work irregularly (such as agency staff) holidays must be exactly that; they can't be replaced by 'holiday pay'. So your employer might owe you additional (paid) days off, rather than actual money. (However, if an informal agreement to the contrary is better for you and your employer, nobody is likely to object).
Chris