Despite the news, UK publishers are continuing to be supplied with magazine publication papers, as merchants and suppliers continue to source alternate routes of supply.
Mechanical coated publication papers remain the hardest hit, with few production facilities outside of Finland.
McNaughton Publishing Papers managing director Simon Varley said his firm's message had not changed from a week ago: "We are continuing to cover all our customers immediate needs, but we have sourced alternative grades from existing suppliers."
Varley said he was working with partners to find a short-term solution to supply. "So far we have not let anyone down."
However Varley did warn that once the mills do return to work it would take a while for normal service to resume, as it would be a question of sorting out what orders are in the system, and what needs to be produced.
The lockouts are providing opportunities for suppliers with production outside of Finland, such as US-based Graphic Communications, which has a UK sales office.
UK managing director Simon Scott said his American colleagues had been bombarded with calls from customers trying to get supply into Europe.
Scott said the mills were being hugely optimistic, as no one had expected the shutdowns to go on this long.
"The grades being produced in the US will allow them to compete more effectively with their European counterparts," he said, with customers spreading their choice and supply of paper.
The lockouts were scheduled to end on 29 June, but will now continue until 7 July.
Despite progress being made on several issues, the key items such as the use of outside sources for some tasks is still proving a sticking point.
Story by Andy Scott