Home Secretary Theresa May requested that the two militant Islamic groups be banned under new anti-terrorism laws, the BBC reported.
If the request is approved by Britain's Parliament, the groups would be banned from operating in the United Kingdom starting Friday. If the groups are banned, showing support for or joining either group would be illegal and punishable by up to 10 years in prison.
The Home Office says Minbar Ansar Deen, also known as Ansar al-Sharia U.K., supports terrorism through the distribution of content on its website. It also encourages members to travel abroad and engage in extremist activity, the Home Office said.
Boko Haram is a Nigeria-based militant Islamic group led by Abubakar Shekau.