The advice does not extend to Hong Kong and Macao.
The Chinese government continues to impose further restrictions on movement within China in response to the outbreak.
It may become harder over the coming weeks for those who wish to leave China to do so.
The FCO said in an update: “If you feel that you may want to leave China soon, you should consider making plans to do so before any further restrictions may be imposed.
“Due to increasing travel restrictions and difficulty accessing medical assistance, the FCO is working to make an option available for British nationals to leave Hubei Province.
“This may happen quickly and with short notice.”
The Wuhan authorities closed all transport hubs including airports, railway and bus stations on 23 January. Some shops and amenities are closed; public events have been cancelled and Chinese authorities have advised the public to avoid crowds.
Travel restrictions are also in place in other cities in Hubei Province.
The FCO continued: “The Chinese authorities are focused on tackling the impact of the virus in different ways, many of which are likely to impact British nationals in all areas of China, not just Hubei province.”
Measures include temperature checks at transport hubs and other locations; quarantine arrangements for travel between different parts of the country; and restrictions on travel between and within cities.
Medical facilities across the country are under significant pressure. Some are not accepting patients and others have long queues.
Many tourist attractions are closed and country’s Ministry of Culture and Tourism has suspended all tour group companies’ activities to prevent the virus spreading further.
Public Health England has offered advice, which can be found here.
The FCO advises travellers comply with any additional screening measures put in place by the local authorities.
