The warning comes in addition to earlier alerts urging British travellers to avoid all travel to the Hubei province.
Officials said earlier the outbreak had now caused more than 100 deaths.
It has spread across China and around the world to at least 16 other countries.
British nationals in Hubei have been urged to leave, if they are able to do so.
“The Chinese government continue to impose further restrictions on movement within China in response to the coronavirus outbreak,” the FCO said in a statement.
“It may become harder over the coming weeks for those who wish to leave China to do so.
“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.”
The latest advice does not include Hong Kong and Macau.
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.
“This may happen quickly and with short notice,” the government body warned.
British nationals in Hubei have been urged to contact an emergency number – +86 (0) 10 8529 6600 – if they are in need of assistance or in order to register a desire to leave.
Wuhan authorities closed all transport hubs including airports, railway and bus stations last Friday.
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 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,” the FCO added.
“These 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 in China are now are closed, while the ministry of culture and tourism has suspended all tour group companies' activities to prevent further virus spread.