I've no recent experience of flights from LGW, all our flights in recent years have been LHR to JFK or EWR. Reading TRs, not just Marshy11's, makes me wonder whether there is a policy of lower stocks of alcohol on LGW flights (=holidays) than on LHR (=more likely business) flights.
Poor cleaning for the return flight from the Caribbean can perhaps reflect a more laid-back and relaxed attitude over there which doesn't quite "work" when there's a need for a quick turn-round?
Crew are individuals and as HL points out, can be rostered to fly out of either airport.
My two pennyworth is that food on flights out of LHR is markedly better than the food on the return flights, whether JFK or EWR. This must reflect the catering organisations VS contract with in NY, but it's a pity VS don't look to improve this as it doesn't reflect well. We had a particularly bad return flight a couple of years ago when almost the entire cabin left their meals virtually untouched after the first "ugh" mouthful.
I've often had the odd bit of paper on the floor/in the edge of the seat, nothing much. Worst experience was removing the blanket from its sealed pack and finding it had previously been used as a sick bag. And I'd naively thought they were freshly laundered, trusting soul that I am.
