When the Working Time Regulations were first introduced in 1998 they created a legal right to a minimum amount of paid leave. At that time there was a three month’s qualifying threshold. Later the three months threshold was removed and the basic holiday increased.
The threshold still lives on in the organisational memory – we still see contracts today that say you don’t get any leave during the first 3 months (or some other period) of employment. Whilst employers can prevent staff from taking leave during this period, they cannot prevent at least statutory leave from accruing.
So anyone on a short term contract of employment is accruing statutory leave whatever the contract says and should be able to take the paid leave during their employment or paid for any unused leave when they leave.
For more information on holidays