Dock workers fear that if they accept the transfer there will be a change to working hours and that Drakes would be looking for pay cuts.
One worker said: "The say the loss of container trade due to the recession makes this justified.
"But we believe this is just an excuse to outsource us.
"People may recall that Drake were brought in to break the 1994 dock strike and no doubt they will do the same this time."
Another worker said he was very concerned that Drake could use untrained men to tie up vessels . He said that could lead to a "disaster" or serious injury as it is a skilled job.
Peel and Drake have attempted to soothe these fears earlier this month.
Ian Roots, managing director of Drake said that he has been involved in 40 transfers of staff and that pay and conditions had not been unduly affected.
But there is still uncertainty over pension schemes the company admits.
