By the book, the barrel should rest on the front, bottom of the forestock, and require 3 to 7 pounds to lift up. When released, it should return to the bottom center. If lifted up and right, or up and left, it should also return to the bottom center.
Properly bedded, and meeting these specs, the barrel may rattle a bit if the gun is shaken around.
If the barrel is floatind in the wood, and/or resting into the left or right of the rifle, that is another story. Bedding an Enfield is an art, and not to be entered into lightly.
Many shooters would solid bed the barrels. There are claims as to improving the accuracy of the rifle, but in all the years the 4T (and the no4s and the Cno7s for that matter) have served, and continue to serve in military service, the origional standards still stand.