London’s FTSE 100 index sank more than 5%, with similar declines seen in other European markets.
Earlier, stocks in Asia saw big falls, with Japan’s benchmark Nikkei 225 index closing 4.4% lower.
It followed steep losses in US shares on Wednesday, with the Dow Jones plunging by 5.8%.
In the UK, every single share in the FTSE 100 index was trading lower. Once again, travel companies saw some of the biggest falls, with airline group IAG down nearly 9% and Tui falling 14%.
The travel sector’s problems could be compounded by the fact that the UK government is set to step up its response to coronavirus. This could include banning large gatherings, such as sports events or concerts.
Other companies warning on the impact of Covid-19 on Thursday included:
WH Smith issued a profit warning after the outbreak hit sales in its travel division, which includes store at airports and train stations;
Cineworld shares fell by more than 40%. It said that in a worst-case scenario, there was a risk it might not be able to repay its debts;
Estate agent Savills said the outbreak had caused a big drop in transactions in China and across Asia;
Train and bus firm Go-Ahead Group said the outbreak had affected the number of travellers on some of its services
Elsewhere in Europe, share indexes in Paris and Frankfurt were down by more than 5%.
On Wednesday, Mr Trump announced a ban on travellers from 26 European countries entering the United States for 30 days, starting on Friday, in order to fight the coronavirus outbreak.
In a televised address from the Oval Office, Mr Trump said the restrictions did not apply to the UK.
He also announced financial relief for US workers who are ill, quarantined or caring for others due to the illness. The emergency action will also see the US Treasury Department deferring tax payments without interest or penalties for certain businesses and individuals affected.
At the same time, the US government will provide capital and liquidity to small firms affected by the outbreak.