Someone may be able to build on this!
The following were running on BR Eastern Region in Summer 1955:
1. Harwich (Parkeston Quay) to/from Liverpool (Central) (not named in 1955 TT)
Weekdays only. Connected with night service to/from Hook of Holland.
2. Harwich (Parkeston Quay) to/from London Liverpool St. 'The Hook Continental'
Every day. Connected with Night Service to Hook of Holland 'Royal Mail Route' (BR)
Relief services also ran Weds/Fri from Liverpool St and Thurs/Sat from Harwich during July and August.
3. Harwich (Parkeston Quay West) to/from London Liverpool St. 'The Day Continental'
Every day. Connected with Day Service to Hook of Holland 'Royal Mail Route' (Zetland Steamship Co.)
4. Harwich (Parkeston Quay) to/from London Liverpool St. 'The Scandinavian'
2-4 days per week across the TT. Connected with service to Esbjerg 'Royal Danish Mail Route' (United Steamship Co. Ltd. of Copenhagen)
Here is what ran on Tuesday 25 July 1989, to pick a busy summer day. LST is London Liverpool St, HPQ Harwich Parkeston Quay.
1A66 09.35 LST-HPQ (10.44) for 11.15 sailing to Hoek van Holland
1A24 13.25 LST-HPQ (14.41) for 16.00 sailing to Kristiansand
1A36 15.03 LST-HPQ (16.20) for 17.00 sailing to Esbjerg
1A42 16.20 LST-HPQ (17.34) for 19.30 sailing to Gothenburg
1A62 19.35 LST-HPQ (20.43) for 21.45 sailing to Hoek van Holland
1A63 07.45 HPQ-LST (09.01) 06.45 arrival from Hoek van Holland
1A35 13.15 HPQ-LST (14.29) 12.30 arrival from Esbjerg
1A39 14.00 HPQ-LST (15.17) 13.00 arrival from Kristiansand
1A53 17.40 HPQ-LST (18.57) 16.30 arrival from Gothenburg
1A67 18.45 HPQ-LST (19.55) 17.45 arrival from Hoek van Holland
There were relief trains to 1A66 and 1A62 as well. The Hamburg ship ran on opposite days to the Esbjerg service at this time of year.
These days trains still run to and from Harwich International for the Hoek sailings, but are mostly part of the normal timetable with intermediate stops.