Within the UK
Sopra Steria, which runs all UK Visa and Citizenship Application Centres within the United Kingdom, has the following message on its website:
CORONAVIRUS (COVID-19) UPDATE 1 If you have Coronavirus symptoms and should be self-isolating, or if you have Coronavirus, you must not attend your appointment. Please email firstname.lastname@example.org with ‘COVID-19’ and your UAN in the subject to say that you cannot attend. We will refund your fee and will tell the Home Office.
CORONAVIRUS (COVID-19) UPDATE 2 If after your visit to us, you develop symptoms, or have Coronavirus, please email email@example.com with ‘COVID-19’ and your UAN in the subject and details of your appointment.
Outside the UK
UK visa application centres in China are closed. VFS Global, which runs the centres, has stated that it is returning passports held in those visa application centres to customers by courier where requested. Those who want to ask for their passport back can “contact VFS Global directly by emailing firstname.lastname@example.org discuss available options. Please include your GWF number and the city where you made your application in your email”.
VFS has a dedicated coronavirus page listing application centre closures worldwide. As of 17 March 2020, it reports that:
The UK has stopped accepting visa applications in China (except Xi’an), Tehran (Iran), Kuwait City (Kuwait), Manila (the Philippines), Ulaanbaatar (Mongolia), Kingston (Jamaica), Georgetown (Cayman Islands), Bridgetown (Barbados), Nassau (Bahamas), Castries (St Lucia), Lima (Peru), Caracas (Venezuela), and Albany and, Fargo, Virgin Islands, Oakland, Santa Clara, San Francisco, Salinas, Santa Rosa in the (US), Quito, Guyaquil (Ecuador), North Mumbai (India), and Hamilton (Bermuda).
In addition, it says that the “UK has stopped accepting Priority Visa applications in Japan, Indonesia, Australia, New Zealand, Fiji, Papua New Guinea, South Korea, Malaysia, Philippines, Singapore, Taiwan, Hong Kong and Brunei”.