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Hugh,
The CLIP entry for Catherine (of Arundel) ON 25857 notes the port of registry from Melbourne 1854,
to Falmouth 1860, then Arundel from 1861 >.
From 1865 the owner is recorded as T. Cunningham, Littlehampton (Mercantile Navy List 1865 p.60).
I had a quick look at LLoyds Register of Shipping @ 1853-55 but selecting the appropriate vessel was a little uncertain.
A longer search from 1854 to 1865 in LRofS might lead you to the owner(s) for that period or if it is for a later period the LRofS will give you details.
jcmac.

I have extracts from The National Archives from BT98/3745 with reference to a ship name "Catherine" of Glasgow ON--- as follows:-
Catherine (of Glasgow) ON----. 198 tons    30/1853   voyage 22.7.1853 - 14.1.1854,
Catherine (of Glasgow) ON----, 198 tons    22/1854   voyage 14.2.1854 -  ...........  ,

I have attempted to identify the continuing record/identity of the ship from the "CrewListIndexProject" and "Lloyds Register of Shipping" but with no success.
I was unable to confirm if it did remain to be given an Official Number - or some other event intervened !?

Over yesterday and today I happened on the CLIP pages of "Ships pre-1855" and reference to a Glasgow ship -,
Catherine
 30/1853. 198tons Registry transferred to Belfast 9/1854. TNA,BT111/29-4,image6,row6.
 
 22/1854, previously Belfast                                           TNA,BT111/29-4,image6,row68.
   9/1854.     9/1854 Catherine (Glasgow 22/54 Belfast) 198tons
 
 22/1854,  Registry transferred to Melbourne 1854.           TNA,BT111/29-4,image6,row69.

Belfast ship -,
Catherine
   9/1854,  previously Glasgow          30/1853                   TNA,BT111/29-4,image6,row6.
   9/1854, 198tons  Registry transferred to Glasgow 22/1854  TNA,BT111/29-4,image6,row68.
 
Can anyone suggest what these details actually indicate and if the Registry to Melbourne has taken the ship abroad; if a change of name occurred: if it remained in UK
jcmac.                                           
     

last part-
12 Woodside Place, Bowling

Whiteinch was not part of Glasgow in 1881.
I think it was part of Renfrewshire (or Govan).
jcmac.

I used the NZ papers to track this vessel and because of the difficulty in using a limited number to search I committed to All/All in the newspaper selection. A very,very long list of searching!!!!! 
The story of its move in/out of the Med is repeated constantly in the majority of the NZ papers - I had no reason to doubt these reports - only why, having been sunk, it was still recorded as sailing up to 3 years later
Mystery solved thanks to RC members.
jcmac.