On 'normal service' days, 'one' run direct trains between London Liverpool Street and Harwich International, to meet the busiest ferry sailings and arrivals. At other times, it's necessary to change trains at Manningtree.
However, Network Rail are mid-way through an upgrade programme on the London-Norwich line. This is scheduled to take approximately 10 years to complete. During this period, the line is closed at some point between London and Norwich on almost every Sunday and on most Bank Holidays as well.
May 28 is a public holiday so, almost inevitably, part of the track is closed for engineering work. (This time, its the section between Colchester and Witham). This means that the journey from Harwich International to London requires travellers to take a branch line train between Harwich and Manningtree before transferring to a mainline service to Colchester. From there it's a bus to Witham, where train services resume to Liverpool Street.
I used to run a railway station in that area and I had to give out similar information, week after week, for several years. I can only tell you what I had to tell them: There's no alternative route, so you'll just have to struggle, with your cases, on and off the trains and buses. Sorry!
Chris