The firm has entered into a period of consultations with the site's 92 staff.
"It is with great regret that we now propose to close the Luton site, but continued production at Luton is unsustainable," said Wyndeham Press Group chief executive Paul Utting.
Work from the two sheetfed sites will either be moved to Wyndeham Grange, other group sites or outsourced via the firm's print management arm, Bespoke.
The announcement comes less than two years after Wyndeham bought litho and digital large-format specialist Blacketts for £5m and a little over a year after it moved it from its Epping site to share Westway's Luton facility.
"In order to operate competitively, we have had to evaluate our multi-site operation and consolidate areas of our business," said Utting.
The intended closure of Westway and Blacketts follows a turbulent year for the group’s sheetfed sites, which included the closure of Hubbard and the redundancies at Impact last summer.
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