Am I entitled to holiday pay?

So I'm quitting the job I've had whilst I've been in 6th form (17-19 as I retook a year) and have asked for my holiday pay as I have had absolutely nothing. I worked out I should have around £340 for 'casual or irregular' hours. However my boss has now said I'm not entitled to it because I'm in full time education and don't pay tax. I can't find much online about this and so before I ask anyone more professional I thought I'd ask to see if anyone on here has been in a similar situation. I used to get holiday pay when I worked at Butlins after year 11 for the summer however she said I wasn't entitled to that it was just because they were a large company they could afford it whereas this is a small local business and it's optional unless I'm not in school and work over 3 days a week. I'm 18.

Do you have a contract?
If so, what does it say about holiday pay?

Yes, you are entitled to paid holidays. Your status in education or whether or not you are over the tax threshold is irrelevant.

There is a calculator on the. gov website which will tell you how much you're owed. If your workplace refuse, then consider taking them to an employment tribunal.

I used the calculator however boss insists that it doesn't count if I'm in full time education and says I have to work at least 3 days a week every week to be entitled to it. My mum is an accountant for an employment lawyer so she's going to ask him - just wish I could have it without all the effort!

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If you've worked there 2 years surely you've had holidays in the past. Were you ever paid for these?

I used the calculator however boss insists that it doesn't count if I'm in full time education and says I have to work at least 3 days a week every week to be entitled to it. My mum is an accountant for an employment lawyer so she's going to ask him - just wish I could have it without all the effort!