Students in the UK are liable to pay income tax and national insurance contributions on their earnings, and have a tax-free personal income tax allowance just like everyone else. The personal allowance is £12,500 in 2020/21. So, if your earnings and other taxable income are lower than this allowance then you should not pay income tax. (Student loans, grants and other allowances are not taxable).
If you think that you will earn less than your allowance from holiday work, you can ask your employer for form P38(S) and you will not pay income tax on your earnings. If you already have a part-time job during term-time, you won't be able to use this form just for your holiday job, but your employer should ensure that you don't pay too much tax.
Use the Tax Checker if you think that you have overpaid tax during the year contact HMRC.