The FCDO has updated its guidance on Ukraine. The relevant link is here: Register your presence in Ukraine with FCDO | FCDO | GOV.UK with the full guidance copied below.
Consular and Visas
The safety and security of British nationals is our top priority. We therefore advise British nationals to leave Ukraine immediately if they judge it is safe to do so. It is for individuals to make that decision, whilst following the advice of the Ukrainian authorities, as measures will vary from region to region.
You will be aware that British Embassy Kyiv colleagues have temporarily relocated to Lviv, where we can issue documentation and provide in-person consular assistance to British nationals and their families.
We are not currently able to provide any in-person consular support elsewhere in Ukraine. However, we continue to provide 24/7 support remotely. If any British nationals require consular assistance, they should call the FCDO on 01908 516 666 or +380 44 490 3660.
The vast majority of British nationals in Ukraine will not need our direct assistance. We have, however, set up a registration system (https://www.register.service.csd.fcdo.gov.uk/ukraine-20220121/register-your-presence-in-ukraine-with-fcdo) so that we can continue to send regular messages, including any updates to Travel Advice. British nationals remaining in Ukraine should register on this system and sign up for Travel Advice email alerts: https://www.gov.uk/foreign-travel-advice/ukraine/email-signup.
The large numbers of Ukrainians fleeing the country has resulted in long queues at the border. We are not able to expedite individual border crossings on the Ukrainian side, but can speak with the Ukrainian authorities if there are systemic problems (e.g. documents not being recognised). Rapid deployment teams of FCDO staff have been deployed to neighbouring countries in order to support British nationals in need of consular assistance once they have crossed the border.
We are working closely with the Home Office to ensure that British nationals are able to access support quickly.
The FCDO remains responsible for issuing emergency travel documents. These can be issued and collected from Lviv. Anyone requiring an emergency travel document can do so via GOV.UK or call the consular assistance numbers above.
The Home Office continue to hold responsibility for visas and passports. The Government has taken measures to ensure that those with family ties to the UK are able to join their families in the UK. Concessions have been made to the family rules to allow Ukrainian family members of Settled persons or British Nationals to come to, or remain in, the UK when they would otherwise not meet the core requirements of the family rules. Changes to Immigration Rules will come into force from 15 March, with a bespoke application process open from Friday 4 March. Family members of British nationals in Ukraine who wish to apply for a visa under the Family Migration route should call 0300 3032785 for assistance before making an application. This is a dedicated line. Further information can be found here: https://www.gov.uk/guidance/support-for-family-members-of-british-nationals-in-ukraine-and-ukrainian-nationals-in-ukraine-and-the-uk.
FCDO consular staff provide a dedicated hotline for Parliamentarians for urgent consular and emergency travel document constituency cases: 020 7008 0999.
Written enquiries should be sent to FCDO.correspondence@fco.gov.uk.