The news comes as it prepares to open 10 more sites on July 16, including its flagship shop in Oxford Street. The others reopening are Basingstoke, Cardiff, Chelmsford, Chester, Edinburgh, Exeter, Glasgow, Stratford and the Trafford Centre in Manchester.
Up to 19 stores could be up for the chop, although the partnership has said more of those currently shut will open over the summer.
At the start of the pandemic, insiders warned it was unlikely all department stores would reopen after lockdown ended.
The partnership has cut costs by £100m, including a reduced spend on advertising that puts its annual tear-jerking Christmas television advert in danger.
It has also put 14,000 staff into a taxpayer-backed furlough scheme – more than half the John Lewis workforce. Waitrose employs about 51,000 people. It is also saving millions of pounds though a year-long holiday from business rates.
Dame Sharon said: “We entered the crisis with weakening profits, and we have taken a number of actions to preserve cash.
“Support from the Government has been a big help – they have paid most of our furlough costs and given us a holiday from business rates.
“Trade too has not been as bad as our worst-case scenario thanks to a lot of hard work from our partners. However as our competitors reopen we expect trading to be tougher in the second half of the year.”
Stores in danger of not reopening include Aberdeen, Ashford, Birmingham, Brent Cross, Chichester, Croydon, Heathrow, Leicester, Newbury, Oxford, Peterborough, Reading, Sheffield, St Pancras, Swindon, Swindon Outlet, Tamworth, Watford, and White City.
In a sign that the crisis is even hitting luxury retailers, Harrods is also axing close to 700 jobs.
Chief executive Michael Ward told staff in a memo: “Due to the ongoing impacts of this pandemic, we as a business will need to make reductions to our workforce.
“I am sorry to say that after exploring every option available, we now recognise that we need to make changes to our operational structure.”
Separately, Arcadia said: “We deeply regret the impact this will have on those individuals affected and will do everything we can to support them.”