Student visas
This visa has replaced the Tier 4 (General) student visa. If you are an undergraduate registered on a UK course, and are expected to return to your studies, it is normal for you have the right to work in the UK out of term time without a work permit. If any employer requires further information you should refer them to the UK Government Home Office website. There is a general page which covers visa and immigration here.
A student visa issued for full-time degree level studies allows you work full-time during official vacation periods. Visit the University International Students office for advice on working on a student visa. Intermitting from the course for employment is not permitted on the Tripos.
National Insurance Number
When you work for an employer, it is a legal requirement for you to pay Income tax and National Insurance. If you are not a UK resident, you will need to apply for a National Insurance (NI) number. This is sometimes printed on the back of your biometric residence permit (BRP). You do not need to apply for a National Insurance number if you already have one or one is printed on your BRP.
To apply for a National Insurance number, you need to visit the HM Revenue and Customs website: https://www.gov.uk/apply-national-insurance-number. An appointment to request an NI number will only be granted if you are in the UK.
You may end up paying too much tax as you are unlikely to earn the required amount to meet the annual tax threshold. To get this money back, you may be able to claim a refund from the HMRC.