Hi Kaz85uk,
The iPhone User Guide below shows how to rearrange the songs on the playlist created on your iPhone. I've highlighted the key information for you. Click on the link for complete details.
iPhone User Guide - Playlists
Create playlists to organize your music. If you’re an Apple Music member, tap My Music, tap Playlists, then tap New Playlist. (If you’re not an Apple Music member, tap Playlists at the bottom of the screen.) Enter a title, then tap Add Songs. Select songs and albums to add to the playlist. The most recently changed playlist appears as the first choice when you add songs to a playlist.
You can also tap 
next to a song or album, tap Add to a Playlist, then tap New Playlist.
To customize your playlist’s artwork, tap 
, then take a photo or choose an image from your photo library.
Share a playlist. To share a playlist, tap next to it, tap 
, then choose a sharing option.
View particular playlists. In addition to playlists you create, Playlists includes playlists you added from Apple Music, as well as those shared with you. To view just the playlists you created, tap All Playlists, then tap My Playlists. You can also choose to see just Apple Music Playlists or only the playlists saved on iPhone.
Create a Genius playlist. In My Music tap next to a song, then tap Create Genius Playlist.
Edit a playlist you created on iPhone. Select the playlist, then tap Edit.
-
Add more songs: Tap Add Songs.
-
Delete a song: Tap 
, then tap Delete. Deleting a song from a playlist doesn’t delete it from iPhone.
-
Change the song order: Drag 
.
New and changed playlists are added to iCloud Music Library and appear on all your devices if you’re an Apple Music member or iTunes Match subscriber. If you’re not a member or subscriber, they’re copied to your music library the next time you sync iPhone with your computer.
Delete a playlist you created on iPhone. Tap next to the playlist, then tap Delete from My Music.
Take care,
