Unfortunately most will not. According to the Association of British Insurers:
Only a very small number of businesses choose to buy any form of cover that includes business interruption due to a notifiable or infectious disease. Usually these extensions list very specific diseases that are covered, not any notifiable disease that may emerge such as COVID-19. An even smaller number will have cover where the notifiable or infectious disease is unspecified enabling them to potentially claim for the impact of the Coronavirus pandemic. However, such policies often respond only when the disease is present at the premises as they cover the interruption to trade caused where business premises have been infected by an illness such as Legionnaires’ disease or norovirus and where the building needs to be closed and cleaned to deal with the specific incident.
Speak to your insurer directly to confirm whether or not you are covered.