Are all the shops in central London, closed in lockdown, still paying rent to the Duke of Westminster?

Answer 1

Do you have a lease?  If so it is a good idea to read it.  Have a little chat with your bank.  They may tell you about the way business works.

Answer 2

No. They pay their rent to the Grosvenor Estate, which is a separate entity. Many businesses are expected to renegotiate their leases with the landlord. 

Answer 3

Everyone has to pay their bills, even shops that closed in lockdown.