The Society of London Theatres say that if you have booked through a ticket agency or directly with a theatre they will be in touch with you BUT be patient. It will take time. You should get refunds.
If you booked with a credit card DO NOT contact the card company as that will slow things down.
PLEASE NOTE
If your booking are for AFTER 26 April DO NOT contact them. It may be that there will be no need but if closures last beyond that date they will be in touch.
I would imagine this applies to theatres throughout the country.
There will be on line performances you can view - check the Royal Opera House web site which should tell you what they are planning to transmit.