In both cases the cost of oil has played a key part, with suppliers citing the rising cost of paper chemicals and increased energy and distribution costs.
Premier Paper Group chief executive Martyn Eustace said mills were already advising of increases, which they appear determined to push through.
Woodfree reels have already been affected, and Eustace said his firm would increase the price of sheets this month.
PaperCo increased carbonless and text and cover prices on Monday (4 April). Managing director Alistair Gough said: "Prices are entering a phase of upward movement, due to the unacceptable level of returns being made by all the main paper manufacturers."
Antalis will increase its price on paper, envelopes and packaging, by between 4-8%, from 25 April.
Manufacturers Sappi and Ahlstrom will raise prices of flexible packaging and label papers from 1 May by 55 (e80) per tonne.
Ink prices are set for further rises due to global shortages of raw materials, the British Coatings Federation has warned.
BCF director Moira McMillan said it was not a case of the ink industry "crying wolf". "It is our duty to flag up potential cost rises for our customers," she said.
Story by Andy Scott and Josh Brooks
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