Vanguard was in operation at that time but remained in home waters as a deterrent to possible Soviet Navy aggression during the Korean War.
British ships sent to Korea were light cruisers, first Ceylon, and then Belfast along, with several destroyers. These British warships (and some Dutch warships) carried out bombardments operating without USN forces and with USN forces at different times. During some operations the joint task force flag ship was Belfast (flying the flag of Admiral Moncreif), the only time the New Jersey was ever under Royal Navy command.
The battleships used off Korea were only Iowa class, used in rotation. First was Missouri because it was the only one in operation when the crisis flared up. Following Missouri's tour of duty it was relieved by the New Jersey.
New Jersey did not arrive on station until 17 May 1951 leaving two months that the combined forces did not have a battleship. During its first bombardment operation it was hit twice by return fire from N. Korean shore batteries. One hit turret number 1. There was no penetration as far as I know but the forward ammunition handling room inside was destroyed. The other hit killed one sailor and wounded three others with splinters.
During July, New Jersey suffered a major machinery breakdown to the number 3 turbine while operating with carriers at high speed. Oil pressure was lost and bearings destroyed. New Jersey limped into Yokosuka Japan were temporary repairs were made by the repair ship Ajax before returning to the firing line until it was relieved by Wisconsin during Dec 1951. New Jersey was sent to Norfolk Naval Yard for a thorough overhaul lasting six months.
Wisconsin was in turn relieved by Iowa on April 1st 1952 after BB64 had been hit by a 6-inch shore battery a week earlier.
Iowa and HMS Belfast carried out a joint bombardment using RN spotter planes during June 1952. During Sept the Iowa destroyed a train that had been previously stopped by the RN destroyer HMS Charity. Iowa was in turn relieved by Missouri during Oct 1952.
During March 1953 the Missouri's Captain Edsall suffered a massive heart attack and died on the bridge.
This was followed by New Jersey's second tour until the end of hostilities.
Entering a night sea battle is an awesome business.The enveloping darkness, hiding the enemy's.. seems a living thing, malignant and oppressive.Swishing water at the bow and stern mark an inexorable advance toward an unknown destiny.