Travelling FROM the UK
Under current UK COVID-19 restrictions, you must stay at home. You must not travel, including abroad, unless you have a legally permitted reason to do so. It is illegal to travel abroad for holidays and other leisure purposes. Stay up-to-date: https://www.gov.uk/guidance/travel-advice-novel-coronavirus
The Foreign, Commonwealth and Development Office recognises some people may have essential family and/or business travel. If you have a family emergency and need to urgently care for a loved one when no one else can, this could be considered essential travel.
FCDO travel advice explains that you must comply with the restrictions on travel, both domestic and international, that apply in each nation across the UK. You must not leave home or travel, including abroad, unless you have a legally permitted reason to do so. It sets out the risks that you may face if you go to another country, including non-COVID risks, if you are able to travel abroad.
If you must travel you should purchase comprehensive travel insurance, and make sure you are content with the level of cover it provides, due to the constant changing effect of the pandemic. If you already have travel insurance check it is valid and provides appropriate cover.
If you are legally permitted to travel abroad, check the advice on your country of destination. Some other countries have closed borders, and may further restrict movement or bring in new rules including testing requirements with little warning.
Travelling INTO the UK
If you intend to travel to the UK from abroad, including UK nationals returning home, you must provide evidence of a negative COVID-19 test result taken up to 3 days before departure. If you do not comply (and you do not have a valid exemption) your airline or carrier may refuse you boarding and/or you may be fined on arrival.
Before you enter the UK you must provide your journey and contact details. You must self-isolate (or quarantine) when you enter the UK from any foreign country except Ireland, unless you have a valid exemption.
When you enter England from abroad (except Ireland), you must follow the new requirements for quarantining and taking additional COVID-19 tests. You should check the country page for more information. If you are travelling from a country on the banned travel list you must quarantine in a hotel. Different rules apply for arrivals into England, Scotland, Wales and Northern Ireland.