It keeps prayer fresh and focused when you have approximately 15 minute slots on topics, so choose amongst the topics below:

Start with Worship. This lifts people’s eyes on Jesus and stirs faith. It doesn’t have to be a band. It could be a psalm or other portion of scripture followed by thanksgiving, one person on a guitar, etc.

Use a video. This is a great video to start and explains something about Muslim people, and God’s heart for them: http://prayercast.com/ishmael.html
Another option would be to use an excerpt from http://morethandreams.org/
There are many other reliable videos you can find on the internet.

Do you know of any local outreaches? Share encouraging testimonies of ministry among Muslims, local ones if possible. Do you have anyone local who can share for 3 minutes about what is happening and to suggest prayer pointers?

If not, pray for the Christians involved in local or regional outreach to Muslim people: that they might reflect the beauty of Christ in all their dealings with Muslim people. Pray for the Holy Spirit to be preparing the ground amongst the Muslim population in that area for seed to be sown and a harvest to be grown.

Pray for personal contacts. Write their name and their need, and place it in a box. Then each person takes a name out of the box and prays for it individually. When they are finished praying they take another one. This can continue as long as you wish.

Invite a Believer from a Muslim background to share a testimony, or some of their struggles so you can pray for them.

Prepare the names of local mosques and their location. Pray for the development of connection and engagement with church leaders in their area.

Current news events that are impacting Muslims in the UK.

Pray for the work of SAT 7 which beams the message of Jesus into many Arabic-speaking countries https://sat7.org/ . See also Pak7 https://pak7.org/.