At present, the rights and status of EEA nationals in the UK remain unchanged. There are further details on the gov.uk webpages here: https://www.gov.uk/guidance/status-of-eu-nationals-in-the-uk-what-you-need-to-know
If you are an EEA national (a person whose country is a member of the European Economic Area) you do not need a visa to enter the UK, however if you want to live in the UK for more than three months, you must be a 'qualified person'. A qualified person means an EEA national who is in the UK as:
Swiss nationals have the same rights of residence as EEA nationals.
If you are a non EEA National you may need a visa to enter the UK. Nationals of some countries do not need a visa if coming for a visit of less than 6 months. You can find out more by completing the UKVI online questionnaire.
If you are visiting the UK for leisure, business, to take part in sports or create events or for another reason such as to receive private medical treatment, you can apply for a Standard Visitor Visa. Your stay is usually limited to 6 months and you are not able to undertake paid or unpaid work on this type of visa.
If you are planning to work in the UK you will need a visa under the UK Border Agency Points Based System, under Tier 1, Tier 2 or Tier 5. Below is a summary of the Tiers.
Tier 1 Exceptional Talent
Tier 1 of the points-based system is intended for 'high value' applicants and is for those endorsed as an internationally recognised (Exceptional Talent) or emerging (Exceptional Promise) leader in their field. Tier 1 visas are not job-specific (i.e. they generally permit the holder to take up any post) and therefore those applying for any type of Tier 1 visa do not require sponsorship from the University.
Tier 2 Sponsored Skilled Worker
To apply under Tier 2 you will need a job offer from a UK Employer along with a Certificate of Sponsorship, issued by HR. Unless you currently hold a visa and you are extending your stay with the same employer doing the same job, you will be required to provide evidence of your qualifications, English language skills and available maintenance. The University will only certify maintenance for you as the applicant, not your dependents, when issuing a Certificate of Sponsorship.
Tier 5 Sponsored Researchers
This falls under the Government Authorised Exchange category, with the University as your sponsor. It applies to researchers, who are being paid from a research council or overseas institution to carry out research that will mutually benefit both the individual and the sponsor. You will need a Certificate of Sponsorship to apply for a Tier 5 visa, and must be able to prove you have had at least £945 in your account at all times for 90 days prior to your application.
You can view more information on all the types of working visas on the UKVI website.
If your family members are Non EEA nationals and you are an EEA National, they have the right to live and work in the UK as you do. To confirm this they may apply for a family member residence stamp, or residence card, although they do not need this to enter, live or work in the UK. Further information can be found at the UKVI website.
If your family members are Non EEA nationals and you have (or are applying for) a visa in the UK, your family may be entitled to apply as dependants. A dependant is usually:
Once they have received a visa, your dependants have the same rights to live and work in the UK as you do. More information can be found on the UKVI website under the 'guidance for dependants' section.