changing db prefix plugin pre parations

So I am building a nice little plugin for myself. The database is working fine . I have made the table using the $wpdb->prefix and it has happily come out with wp_my_table.

So when I upload it to a live site for testing, as it has the database prefix changed, the plugin no longer works with the database.

My $wpdb query only seems to work with SELECT * FROM wp_my_table ORDER desc when I manually adjust this to the new database prefix xxxwp_my_table. How do I get my plugin to auto adjust to the changed table?

I have tried various ‘$wpdb->my_table’ or other such things but they just don’t quite make sense.
Anyone with a heads up on this?