If you have a baby in the UK, you do not need to apply for immigration permission for the baby unless your baby needs to re-enter the UK after travel.
If you are in the UK as a Student Route visa holder, you can apply inside the UK for your baby if you meet the following requirements:
If you do not meet the requirements above, you can apply outside the UK only if you meet the following requirements:
If you are studying for longer than 6 months then you (and your dependants) are entitled to free medical treatment on the NHS.
For more information about entitlements for children, pregnant women or health benefits which may subsidise the cost of NHS prescriptions, dental charges and optical costs visit the NHS website, or UKCISA.
Please note depending on how many weeks pregnant you are some airlines may ask for a letter from your doctor or midwife confirming your due date, and that you are not at risk of complications.
Please check with your airline to ensure you are permitted to travel.