Do I qualify for holiday pay?

Yes, up until recently all employees in the UK were entitled by law to 4 weeks paid leave every year. New holiday legislation has now been introduced and as of April 2009 all employers are required to give 8 bank holidays as paid leave in addition to the 4 weeks. That means that all employees will now be entitled to 5.6 weeks holiday per year.
If you work on a part-time basis and you want to know how many days you are entitled to, simply multiply the number of days you work each week with 5.6.