Bit of a mystery I'm afraid. I managed to have a look at a copy of Jane's Fighting Ships for 1969–70 but there is no HMS Fathomer for any navy. The Royal Navy by that date only had the two Fast Patrol Boats, Brave Borderer and Brave Swordsmen, plus two of the old Dark Class still retained, Dark Gladiator and Dark Hero. The boat in question could presumably have been anything, and if it was a Fairmile of some description, then its identity is not readily apparent. It might have been registered with Lloyd's?
Sorry not to be of any further assistance