GS, there was certainly a 4-engine/2-engine debate over the Atlantic/Shackleton which which favoured the Nimrod over the Atlantic, but then the Nimrod needed 4-engines for much of its mission but was then lugging extra weight for the rest of the time.
Four engines doubles the whole engine logistics costs and with small numbers no economy of scale.
Twin jets are now more reliable, powerful, and economical. For an MPA a sea bird strike is perhaps the only reason for extra engines. Four engines however are no guarantee of survival from a bird strike.