John Lewis, which also runs Waitrose supermarkets, says it will axe up to 1,500 jobs at its head office as it makes further cost cuts.
It says the move will help it to save another £50m as it looks to make £300m in annual savings by 2022.
Meanwhile, Lloyds is cutting a further 730 jobs as part of a major restructuring programme.
The proposed John Lewis Partnership cuts will be made across the two head offices in London Victoria and Bracknell, where John Lewis employs about 5,000 people.
They will come in two phases, the first of which will begin immediately. The second phase will be completed by April 2021.
John Lewis said it would seek to find new roles for staff and, if that is not possible, will offer redundancy support and retraining funds for those with more than two years service.
Partnership chairman Sharon White has set out a five-year recovery plan for the group, which like other retailers has been hit by the Covid-19 pandemic.
In July, the department store division said it would shut eight shops, putting 1,300 jobs at risk, and close four Waitrose stores, with the loss of 124 jobs.
In September, the group told staff they would not receive a bonus for the first time since 1953 after it dived to a £635m pre-tax loss for the six months to July, following a £470m writedown on its stores.
Lloyds cuts 'shameful'
The cuts at Lloyds Banking Group will mainly affect staff in its group transformation and retail banking teams, and will result in no further bank closures, it said.
A Lloyds Banking Group spokeswoman said: "This morning we shared changes to some of our teams.
"These changes reflect our ongoing plans to continue to meet our customers' changing needs and make parts of our business simpler.
"The majority of colleagues briefed today will not leave until January at the earliest."
The Unite union said the move was "shameful", and that the decision was taken despite recent strong results. It called for the bank to postpone restructuring amid the rising threat of Covid-19.
"Unite cannot comprehend why Lloyds Banking Group would choose to cut 1,000 staff who have given the bank such commitment and dedication during a global pandemic," said Rob MacGregor, Unite national officer.
Lloyds posted forecast-beating quarterly profits last month after cashing in on a coronavirus-driven boom in demand for mortgages.
But in July the bank warned that lockdown was having a greater economic shock than expected.
In September, Lloyds said it planned to cut 865 jobs, mainly in its insurance, wealth and retail teams.