I don't think there is a public visible user ID. There is your unique MusicBrainz user name, Lee_Austin.
For what do you need it? I have the feeling you are coming from the BBC Introducing Artists site, right? There was a question about that recently, see
If this is the case you need a MusicBrainz artist ID, not your user ID. You can search for an existing artist or create a new one, see the thread I linked to.
I could not find any existing artist for Mr Beat & The Preacher, so maybe you should just create one with the form at https://musicbrainz.org/artist/create