From what I understand the tube is not busy at all, as its mainly used by essential workers, at the moment. If you are concerned check with one of the members who live there. Katejo does so you could always PM her.
It also depends on the route you need to take. Sometimes you can do it by normal over ground rail routes, rather than the tube.
Also, any chance you can drive, or be driven in. I think the congestion charge has been waived, at the moment.