Good afternoon adambroadbent,
Welcome to the Apple Support Communities!
I understand you are wanting to delete multiple songs from your iCloud Music Library. Although you can't do this on your iPhone, you can use your computer to make multiple selections using the Command key, and those changes would update on your iPhone. This does not apply to music downloaded directly to the device for offline listening.
Take a look at the resources below. I've highlighted some key information here for you. Click on the link for complete details.
Delete songs and videos from your iCloud Music Library
If you're an Apple Music member or subscribe to iTunes Match, your music and video content is stored in iCloud Music Library. When you delete an item from iCloud Music Library, it also deletes from any iPhone, iPad, or iPod touch that uses iCloud Music Library with the same Apple ID.
Take care.