The £1m-turnover company went into administration earlier this month citing a period of tough trading as the reason for the its collapse.
The failure marked the second time the company had gone into administration in little more than a year after being bought back by its previous directors in May 2010.
However, Reflex will now incorporate this business into its group operations and has said it will offer both existing and past customers of The Plain Label Company, the "service, sustainability and cost efficiencies" it offers its existing customers.
None of the company's 13 staff were taken on as part of the deal.
Reflex said, however, that it would contact customers in the coming days and planned to promote its range of products, which include self-adhesive and linerless labels, flexible packaging, shrink sleeves, barcode systems, artwork and reprographics.
A spokesperson for the company said the business was a good fit and a great opportunity to expand its existing offering.
Reflex Labels acquires assets and goodwill of Rivers (Midlands)
Reflex Labels has acquired the assets and goodwill of Rivers (Midlands), which traded as The Plain Label Company (PLC Labels).