Any organisation (including churches) in the UK who wish to use copyrighted music as part of an online streamed service (or activity) are required to have an appropriate license to legally allow them to do so. This is administered by PRS (Performing Rights Society) and is called a Limited Online Music License (LOML). It can be purchased directly from PRS, and to calculate the cost they will need to know estimates of your audience size (number of people viewing), the number of songs used in a service, and the number of services. There are also some reporting obligations, meaning that you may need to regularly submit a report to them about the number of tracks used, audience sizes and frequency of use. It only covers music streamed in and to the UK. If you use music without an appropriate license, and are found to be doing so, you may be subject to action against you by PRS or the copyright holder and / or a backdated claim for music already used.

Visit the PRS LOML page here:

https://www.prsformusic.com/licences/using-music-online/limited-online-music-licence

For more detailed information about online music licensing, and options for free or lower-cost options, download this information sheet (PDF).