The group has begun consultation talks with employees and representatives over the proposed closure of the site, following a strategic review of its manufacturing requirements.
UK managing director Philip Beer said the decision was not one the firm was taking lightly: "The pressure on UK manufacturing means we need to consider difficult options."
Amicus GPMS branch official Steve Ireland said the employees greeted the news with "shock and silence".
However, the age of the factory is a problem that both the firm and union representatives acknowledge.
"I don't know if there's anything we can do to persuade the owner to invest in the site," said Ireland.
European office supplies producer Groupe Hamelin bought John Dickinson for an undisclosed sum last year, from DS Smith. The Sawston unit produces the firm's range of New Guardian and Black n'Red envelope products among others and, if it closes, production would transfer to Groupe Hamelin's other production plants.
John Dickinson employs around 400 staff at its three sites in Sawston, Cambridgeshire, Washington Tyne and Wear and Ledbury in Herefordshire.
The proposed closure follows a halving of the workforce at the firm's Washington plant in January this year, when 45 redundancies were announced.
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"This is a repeat of what happened to 1066 Capital t/a Crystal a year ago. They also never put this company in administration.
We are all still left unable to claim the redundancy and notice pay owed..."
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