Your daughters should keep their P45s and if they are not intending to work in the current tax year again after Xmas, they can send their P45s to the tax office and get any refund due straight away. Some tax offices will send a form for completion, but if your daughters write covering letters saying they will not be working again before 5 April, that is normally sufficient.
For future reference, full-time students can ask their employer for a tax form if they work during the summer holidays, and if they can declare that their total income in the tax year will not exceed their personal allowance (the figure given by Ethel), they should not pay tax in the job. This applies only to the long summer holiday, and not other vacation work.
NI cannot be reclaimed.