From 1st January 2021 the rules has changed for EU citizens visiting, working or studying in the UK.! Newcomers need to apply for a Work Visa or in some cases a Student Visa.
Read more about it here

Eligibility and application for British citizenship for a child born in the UK to non- British parents. Dual citizenship for a child.

One parent is a British citizen or has a settled status

A child is automatically a British Citizen if at least one parent is a British citizen or has a settled status (indefinite leave to remain) in the UK.

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You can apply for a British passport for your child online – Apply for a UK passport 
or you can get an application form at any post office, fill it in and send it by post or by using the Postal passport service at a post office.
The passport fee is £49 for online application and £58.50 for application by post.

Both parents are not from the UK and are without settled status

If both parents are required to have a visa or have pre-settled status on the day of your child’s birth, in this case the child will not automatically become a British citizen.

The child later can be registered as a British citizen as soon as at least one of the parents has been granted British citizenship or settled status.
The registration fee is £1012. You can apply online – Register your child as a British citizen or by post – MN1 application form or use checking and passport service at post offices.

A child can also be registered as a British citizen, as soon as he or she turned 10 years old, provided that the child has been living in the United Kingdom for the past ten years. The registration fee is £1012. Application form for British citizenship registration as a 10 year old child – Form T.

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You may apply for your child’s British passport after you received your child’s British citizenship certificate.

Dual citizenship

Most countries allow their citizens to have multiple citizenship, although some countries have different rules. Check with your embassy, consulate or high commissioners in London. Find your embassy here Embassies.

For example

South Africa Those who wish to have dual citizenship must inform the South African government before submitting their application, otherwise they will lose their South African citizenship.
South Korea Allows dual citizenship only if it is citizenship by birth.
Japan, China, Thailand, India and Indonesia do not allow dual citizenship.