Employees at the Bootle plant began taking strike action in early February over proposed redundancy payments and selection criteria, before being locked out by management on 17 February.
The latest round of meetings took place last Wednesday (29 February) at which the company made an improved redundancy package offer. However, it refused to move on selection criteria.
Unite national officer Steve Sibbald said: "As they wouldn't budge on a number of issues it was put to a secret ballot. Out of almost 140 employees, one voted to accept the offer."
A further meeting is planned for Friday (9 March), while employees at the plant continue to be kept out of the building, with no work produced at the site for almost a month.
Meanwhile, Unite members travelled to Germany last week to meet with Austrian and German counterparts.
Sibbald added: "We had a very productive meeting with our colleagues. In Germany, local representatives have written to the company urging them to settle, while the general secretary in Austria has done the same.
"They have made it clear that if this situation is not sorted as soon as possible it could escalate across Europe."