As I see it . . .
Chapter 9 (Part 2) of the Income Tax (Earnings and Pensions) Act 2003 came into force on 6th April 2007. From that date onwards there appears to have been no doubt that people receiving their pay through 'Managed Service Companies' (= 'umbrella companies') have been deemed to be employees of those companies, since such companies are responsible for paying the relevant PAYE and National Insurance contributions to HMRC:
http://www.hmrc.gov.uk/employment-status/msc.htm
(i.e. you can't be classed as 'self-employed', since you pay both PAYE and 'employed' National Insurance contributions).
Therefore you're entitled to (paid) annual leave:
https://www.gov.uk/holiday-entitlement-rights/entitlement
(All employees are entitled to such leave, even if they're only employed on a casual basis).
As my original post (and the accompanying link) shows, you need to work in a fixed-term contract for 4 years before you automatically become a permanent employee.
For further advice, try calling the Acas helpline:
http://www.acas.org.uk/index.aspx?articleid=2042
(It can take ages to get through but their staff really know their stuff, so it's well worth the wait).