Four Yorkshire stores are affected and members of staff have been informed.
The stores in Yorkshire that are set to close under the Company Voluntary Arrangement, which will require approval from creditors who will make their decision on June 22, are Grimsby, Doncaster, Hull and Skipton.
The full list of store closures is as follows: Altrincham, Aylesbury, Birkenhead, Birmingham, Bournemouth, Camberley, Cardiff, Carlisle, Chichester, Cirencester, Cwmbran, Darlington, Doncaster, Edinburgh Frasers, Epsom, Grimsby, High Wycombe, Hull, Leamington Spa, Lincoln, London Oxford Street, London King William Street, Middlesbrough, Milton Keynes, Plymouth, Shrewsbury, Skipton, Swindon, Telford, Wolverhampton, Worcester.
Two stores are excluded from the CVA proposals - Dundrum in the Republic of Ireland and Beatties in Solihull because they are separate legal entities.
Frank Slevin, chairman of House of Fraser, said: "The retail industry is undergoing fundamental change and House of Fraser urgently needs to adapt to this fast-changing landscape in order to give it a future and allow it to thrive.
"Our legacy store estate has created an unsustainable cost base, which without restructuring, presents an existential threat to the business.
"So whilst closing stores is a very difficult decision, especially given the length of relationship House of Fraser has with all its locations, there should be no doubt that it is absolutely necessary if we are to continue to trade and be competitive."
As part of the CVA process, House of Fraser also plans to relocate its Baker Street head office and Granite House office in Glasgow to new locations to help cut costs.
The company said it expects stores that are scheduled for closure to remain open until early 2019.