Because it is not profitable and or strategically practicable to use this port at any other time. ... Neil.
I can't be sure but our weather is not ideal for crusing and perhaps a bit like some cruise lines move away from the Caribbean in April/May and don't return until after the hurricane season is past might give some clues, plus the amount of business probably is another reason but Southampton will still be in business as it is really much more of an international port than Harwich. Always reminds me of landing the first time in Barbados at the Grantley Adams International airport, I thought they probably had others but in the days of the early 80's that was it !!
Probably because the cruises from Harwich tend to be for northern Europe (yes, I know, not all of them). Northern waters are not too popular once the temperature drops.