Findmypast has this entry under Maritime BMD details:
Registration event: death
Name: FARAGHER, P
Date of death: January 1943
Age: (not given)
Place of death: (not given)
Place of birth: (not given)
Belonging to service: (not given)
Ship's name:Speke
Series:BT334 - Registers and Indexes of Births, Marriages and Deaths of Passengers and Seamen at Sea
Box:0101
Page: (not given)

These records are held at the National Archives, London.

There is a very good list of online sources to go through here:
www.genguide.co.uk/source/Merchant-Navy-Death-At-Sea-Indexes/144/

I am hoping the above "month in Register" for P Faragher is the correct record for your Peter Faragher because there was also a Philip Faragher in the Merchant Navy who died in 1943 - also from the 'Speke' - and is listed on the CWGC website (War dead).

FARAGHER, PHILIP Master 28/09/1943 32 Merchant Navy United Kingdom Block N.K. Grave 85. DOUGLAS CEMETERY (ISLE OF MAN)

He was a Master, died in Sept., so they do look like different men. This is his death record on the same Findmypast section:
Registration event: death

Name:FARAGHER, Philip
Date of death:28 September 1943
Age:32
Place of death:Irish Sea
Place of birth:Manchester
Belonging to service:
Ship's name:Speke
Series:BT334 - Registers and Indexes of Births, Marriages and Deaths of Passengers and Seamen at Sea
Box:0104
Page:6

Thankfully a different Box number.

I think it would be worth following up the "P Faragher" entry, firstly by looking through all those online sources given in the web address above.

Sue