The Met said the request is “based on specific intelligence”.
Scotland Yard wants the ban enforced under section 13 of the Public Order Act. The Act gives the police the power to ban public processions when confirmed by the home secretary.
The Home Office said the application would be carefully considered in the usual way.
Chief Superintendent Peter Terry, said: “We have made this decision based on specific intelligence and information, and our message is clear: we do not want people coming into the areas to attend these events.”
The far-right group plan to march through Walthamstow on Saturday. The ban would also affect neighbouring boroughs including Tower Hamlets, Newham and Islington.
The EDL website said they are “more determined than ever”.
It continues: “We will never be silenced, we will never submit.”
It said it faces “intimidation from both the far-left and their Islamist brethren.”
Tower Hamlets Councillor, Peter Golds told EastLondonLines: “I believe as the EDL are inflammatory, then the Home Secretary is right to consider a ban, if requested by the Commissioner of Police.”
Leader of the Labour Group in Tower Hamlets, Cllr Joshua Peck told EastLondonLines: “The police have asked the Home Secretary to step in and ban this march following specific intelligence on the march, we fully support that request.
“In Tower Hamlets we are proud of our mixed community and our history of unity, those who preach hate have no place in our borough.
“Having faced the threat of EDL marches in Tower Hamlets before we know that the community are united in their opposition to those whose aim is to spread violence and hate.”
There were violent scenes when the group marched in Walthamstow last month. 20 arrests were made with protestors on both sides taken into custody.
Fighting broke out in the demonstration with smoke bombs, bottles and flower pots thrown.
In August 2011 Theresa May blocked the EDL from marching through five boroughs in London. May said all rallies, not just those by the EDL, are banned, to protect “communities and property”.
Police arrested 53 ‘EDL supporters’ on Saturday 20 October in connection with Saturday’s planned march. All were arrested on suspicion of conspiracy to cause public nuisance, the Metropolitan Police said.
15 arrests were made earlier this year at an EDL clash in Whitechapel.