The Queen will also thank NHS workers in a speech to the nation on Sunday, Buckingham Palace says.
The health secretary warns people must "follow the rules" on staying at home and social distancing.
The new Labour leader also says ministers should publish their "exit strategy" for restrictions.
The men are both thought to have been in their 60s and were support staff at Pentonville Prison.
One intensive care doctor describes the reality faced by some UK health workers on the front line.