Parts of Essex and Hertfordshire are also reported to be entering tier three.
Health Secretary Matt Hancock is expected to make a statement in the Commons shortly.
The tier three restrictions would see pubs and restaurants closed except for takeaway and delivery services.
One MP said they were told that cases are doubling every seven days in the capital.
They added that the next review of the tier system would be on 23 December.
Mr Hancock is expected to use his statement to outline the financial support available to the tier three areas.
It follows warnings from London Mayor Sadiq Khan that tier three restrictions could have a “catastrophic consequence” for hospitality, culture and some retail.
What are tier three (very high) rules?