Easiest By car
Cheapest by off peak buses Free if 60 plus
You have to balance lugging luggage on bus/train with connections via london etc. vs car.
try various private taxis or transfer companies.
i.e Titan private hire .co.uk or yellow pages.
do not forget prices are usually quoted 1 way.
We have decides that from north wales car seems to be the best option,tried to get a route by train via London and could not be done the same day?and the National coach it was 6 changes,even looked at a flying option you can fly to London and get a coach transfer if you book it via the cruise company we got quoted £250 each return,probably get a taxi for that? not much help but maybe some one else has found an route?
Just found a train link from the Harwich port web site from Manchester Piccadilly there service is a train which will get you there the current price is £158 each return,suggest you try that with your dates and see what it comes up with?
Harwich is a real swine to reach at the best of times. Best and cheapest is to drive and park or get a relative or friend to take you there and meet you on your return, other than that National Express should be cheaper but so lengthy. You could try finding the bus route to somewhere close and getting "an Airport Taxi" from there, that sounds strange I know but it can cut the time and changes down considerably. Good Luck which ever you choose. Neil.