Thanks, Dicky. The ACP reported 3.0.5 under both the General tab and the System tab. I continued with the update as you suggested and all appears to have gone OK.
Just one strange thing - now under System tab it reports "3.0.8 [Re-Check version]", and the System tab reports "Connection refused". checking the phpBB Forum for "Connection refused" indicates this is due to my host "blocking the outgoing port which is used for the board to check with phpBB to make sure you are up to date" (see this
posting). Has the port number changed between 3.0.4/5 and 3.0.8?