Hi Rudi.
One possibility is to take the night ferry crossing to Harwich. You arrive at breakfast time, so you don't need to worry about accomodation. I've done that 3 times now, the cabins are quite nice and it's not much more expensive than the day crossing.
I've caught the train from Harwich. The station is just by the ferry terminal and the trains run to Cambridge and then London.
But presumably, you want to cycle to London. It looks like there are Sustrans routes that run from Harwich to London:
http://www.sustrans.org.uk/map
My experience has been that the Sustrans routes are mostly on road, but not too busy. If you try the CTC touring and expedition forum, you should be able to find more info. It's more focused on England.
http://forum.ctc.org.uk/
Good luck,
James