If the plan is approved, 2,000 House of Fraser jobs will go, along with 4,000 brand and concession roles.
The stores scheduled for closure, which include its flagship London Oxford Street store, will stay open until early 2019, House of Fraser said.
The retailer needs the approval of 75% of its creditors to go ahead.
Creditors will vote on the insolvency plan, which involves company voluntary arrangements (CVAs), on 22 June.
In May, House of Fraser's Chinese owners Nanjing Cenbest reached a conditional agreement to sell a 51% stake to the Chinese owner of Hamley's, C.banner. The sale is conditional on the restructuring plan being approved.
House of Fraser chief executive Alex Williamson told the BBC that the decision to close the shops was "brutal".
"This is as tough as it gets, and we have not taken this decision lightly," he said. "It is very dramatic for people that we care about a great deal."
"I find it personally very emotional, and I am not making this decision based on anything other than what I consider to be absolutely the best option for House of Fraser and all of our stakeholders."